FRACTALS (fractals)

2021 - 2026

Current editor(s): Tara Taylor

From World Scientific Publishing Co. Pte. Ltd.
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Volume 34, issue 05, 2026

ON THE FINITE DELAYED FRACTIONAL DIFFERENTIAL EQUATION VIA THE WEIGHTED RIEMANN–LIOUVILLE DERIVATIVE OF VARIABLE ORDER pp. 1-11

Fahd Jarad, Thabet Abdeljawad, Mohammed Said Souid, Abdelhamid Hallouz and Manar Alqudah

MULTIPLICATIVE FRACTIONAL SIMPSON-TYPE INEQUALITIES FOR MULTIPLICATIVELY THRICE-DIFFERENTIABLE s-CONVEX FUNCTIONS pp. 1-15

Xiaoying Xiang, Zhijie Cao and Tingsong Du

GENERATING INNER AND OUTER FRACTALS IN AN ENERGY SUPPLY–DEMAND SYSTEM AT THE HOPF BIFURCATION POINT pp. 1-15

Abbas Khan, Tahir Saeed Khan, Muhammad Marwan and Li Wang

NONLINEAR EVOLUTION CHARACTERISTICS OF THE MUTUAL-EXCITING NETWORK OF ACOUSTIC EMISSION EVENTS AND THE MULTIFRACTAL EARLY WARNING MODEL pp. 1-15

Zhibo Zhang, Jiang Sun, Hongtu Zhang and Jiabao Wang

ON THE AVERAGE STEINER ECCENTRICITY FOR VICSEK NETWORKS pp. 1-7

Cheng Zeng, Daohua Wang, Zixuan Zhao and Qingcheng Zeng

DIMENSION OF MULTI-BRANCH FLOWER NETWORKS pp. 1-7

Yi Lu, Jingjing Chen, Yuxing Gaozheng and Qin Wang

MULTIPLICATIVE TEMPERED FRACTIONAL INTEGRALS IN G-CALCULUS AND ASSOCIATED HERMITE–HADAMARD-TYPE INEQUALITIES pp. 1-23

Abdelghani Lakhdari, Wedad Saleh, HÃœSEYIN Budak, Badreddine Meftah and Fahd Jarad

DERIVATIVES THROUGH PROBES IN REGULAR GEOMETRIC OBJECTS: A DIMENSIONAL EXPLORATION FOR q-SETS IN TIME SCALE CALCULUS pp. 1-38

Mehmet Nä°yazä° Ã‡ankaya

NEW ANALYSIS AND DERIVATIONS OF SIMPSON’S FORMULAS IN MULTIPLICATIVE RIEMANN–LIOUVILLE FRACTIONAL CALCULUS pp. 1-19

Jianqiang Xie, Muhammad Aamir Ali, Chanon Promsakon and Thanin Sitthiwirattham

FRACTAL-FRACTIONAL MODEL FOR AGGLOMERATE-STRUCTURED MATERIALS IN 3D PRINTING PROCESS AND ITS VARIATIONAL FORMULATION pp. 1-9

Yu-Ting Zuo

INVESTIGATION INTO THE VIBRATION BEHAVIORS OF FRACTAL-MODIFIED NONLINEAR OSCILLATOR FOR CANTILEVER BEAMS pp. 1-9

Pinxia Wu, Chen Zhong, Lixiong Wang and Yanping Liu

A FRACTAL-BASED PERMUTATION BELIEF ENTROPY FOR UNCERTAINTY MEASURE IN RANDOM PERMUTATION SET pp. 1-20

Shaolong Liu, Niu Wang, Daijun Wei, Mingli Lei and Ningkui Wang

TEMPERED FRACTIONAL HERMITE–HADAMARD-TYPE INEQUALITIES FOR s-CONVEX STOCHASTIC PROCESSES pp. 1-22

Hong Li, Hongyan Xu, Muhammad Uzair Awan and Badreddine Meftah

GENERALIZED m-s-GODUNOVA–LEVIN FUNCTIONS USING LOCAL FRACTIONAL CALCULUS AND SOME INEQUALITIES pp. 1-16

Rainier V. Sã Nchez C., Armando Garcã A, Jos㉠E. Sanabria and YESSICA N. NÚÑEZ R.

κ-FRACTIONAL CALCULUS OPERATORS AND SOLUTION OF FRACTIONAL KINETIC EQUATIONS INVOLVING THE MULTIVARIATE κ-MITTAG-LEFFLER MATRIX FUNCTIONS pp. 1-16

Muneera Abdullah Qadha, Sarah Abdullah Qadha and Thabet Abdeljawad

FRACTAL STUDY ON GAS PERMEABILITY IN UNSATURATED DUAL-POROSITY MEDIA BASED ON SOLID–LIQUID CONTACT ANGLE MECHANISM pp. 1-18

Zihang Wu, Shanshan Yang, Xiuya Guo, Huili Wang and Qian Zheng

DYNAMICAL BEHAVIORS AND DIVERSE SOLITON SOLUTIONS FOR THE FRACTIONAL YAJIMA–OIKAWA EQUATION pp. 1-18

Kang-Le Wang

FRACTIONAL- AND INTEGER-ORDER ANALYSIS OF m-SUPERQUADRATIC STOCHASTIC PROCESSES WITH APPLICATIONS IN INFORMATION THEORY pp. 1-24

Dawood Khan, Saad Ihsan Butt, Mohammed Alammar and Youngsoo Seol

QUALITATIVE ANALYSIS OF THE FRACTAL COMPLEX HIROTA-DYNAMICAL MODEL FOR OPTICAL FIBER COMMUNICATION: VARIATIONAL PRINCIPLE, HAMILTONIAN AND DIVERSE SOLITON SOLUTIONS pp. 1-12

Youxian Zhang, Chao Zhang and Kang-Jia Wang

ANALYSIS OF THE EFFECT OF MUSIC TEMPO ON SKIN AND FACIAL MUSCLE ACTIVITY pp. 1-10

Anupam Baliyan, Riya Chauhan, Michal Schmirler, Norazryana Binti Mat Dawi and Hamidreza Namazi

ZERO-HOPF BIFURCATION ANALYSIS IN INTEGER- AND FRACTIONAL-ORDER ENERGY SUPPLY-DEMAND CHAOTIC SYSTEM pp. 1-17

Huimei Liu, Feng Li, Gauhar Ali and Muhammad Marwan

COMPLEXITY-BASED COUPLING OF CARDIAC AND FACIAL MUSCLE RESPONSES TO OLFACTORY STIMULI pp. 1-13

Mohammad Sidiq, Loveleen, Najmeh Pakniyat, Alireza Khalili Golmankhaneh, Shakir Khan and Hamidreza Namazi

EXPLORING THE TIME-FRACTIONAL BLACK–SCHOLES MODEL USING CAPUTO DERIVATIVE: A NUMERICAL PERSPECTIVE pp. 1-13

Xiankang Luo, Amra Al Kenany and Meshal Shutaywi

Volume 34, issue 04, 2026

COLOR IMAGE ENCRYPTION THROUGH MULTI-S-BOX GENERATED BY HYPERCHAOTIC SYSTEM AND MIXTURE OF PIXEL BITS pp. 1-29

Nawres A. Alwan, Suzan J. Obaiys, Nurul Fazmidar Binti Mohd Noor, Nadia M. G. Al-Saidi and Yeliz Karaca

A WAVELET MODELING OF CORRELATED NOISE IN SMART HEALTH MULTI-SENSORS DATA MONITORING pp. 1-10

Anouar Ben Mabrouk, Zaid Bassfar, Fehaid S. Alshammari, Sarah Bassfar and Abdulaziz Alanazi

SOME CHARACTERIZATION RESULTS FOR NONSMOOTH INTUITIONISTIC FUZZY OPTIMIZATION VIA SYMMETRIC gH-DIFFERENTIABILITY pp. 1-10

Yanrong An, Yating Guo, Wei Liu and Huiyun Li

FRACTAL FEATURE MODELING: MULTI-DIMENSIONAL ATTENTION AND SPATIAL ADAPTIVE RELATIONSHIP LEARNING FOR PERSON RE-IDENTIFICATION pp. 1-18

Mingfu Xiong, Hanmei Chen, Yeliz Karaca, Abdul Khader Jilani Saudagar, Ik Hyun Lee, Javier Del Ser and Khan Muhammad

ABUNDANT SOLITONS SOLUTIONS OF THE (2+1)-DIMENSIONAL KADOMTSEV-PETVIASHVILI-MODIFIED EQUAL WIDTH MODEL pp. 1-18

Tooba Shafique, Ravi P. Agarwal, Pshtiwan Othman Mohammed, Muhammad Abbas, Miguel Vivas-Cortez, Tahir Nazir and Abdelhamid Mohammed Djaouti

FRACTIONAL MODELING AND DESIGN ON CONTROL SYSTEM OF 2–DOF LOWER–LIMB EXOSKELETON ROBOT MODEL pp. 1-18

J. E. Lavã N-Delgado, M. C. Salgado-Pineda, J. F. Gã“mez-Aguilar, D. E. Urueta-Hinojosa, M. A. Rivera-Martã Nez, J. E. Mota-Cruz and M. A. Valois-Flores

WAVES PROPAGATION AND SENSITIVITY VISUALIZATION FOR THE FRACTIONAL ORDER HEIMBURG MODEL IN BIOMEMBRANES AND NERVES pp. 1-16

Tahira Sumbal Shaikh, Muhammad Zafarullah Baber, Nauman Ahmed, AKGÃœL Ali, Naveed Shahid, Thabet Abdeljawad, Aiman Mukheimer, Qasem Al-Mdallal and Manar A. Alqudah

A NEW ANALYSIS OF THE AB-FRACTAL-FRACTIONAL OPERATORS USING THE GENERALIZED GAMMA FUNCTION IN GEOMETRIC PATTERNS pp. 1-23

Rabha W. Ibrahim, Dumitru Baleanu, Yelä°z Karaca and Soheil Salahshour

REVIEW ON FRACTAL INTERPOLATION FUNCTIONS pp. 1-32

T. M. C. Priyanka and A. Gowrisankar

STABILITY OF SYNCHRONIZATION MANIFOLD IN COUPLED FRACTIONAL-ORDER NONLINEAR OSCILLATORS: A MASTER STABILITY FUNCTION APPROACH pp. 1-15

Karthikeyan Rajagopal, Sajad Jafari, Prakash Duraisamy, Salah Boulaaras, Anitha Karthikeyan and Asma Alharbi

THE FOURTH-ORDER EXPLICIT GROUPING METHOD BASED ON CRANK–NICOLSON APPROACH FOR SOLVING THE TWO-DIMENSIONAL FRACTIONAL MOBILE/IMMOBILE EQUATION pp. 1-15

Muhammad Asim Khan, Norma Alias, Ayesha Ayub, Umair Ali, Dennis Ling Chuan Ching, A. F. Aljohani, Ilyas Khan and Abid Ali Memon

HUMAN–COMPUTER DIALOGUE SYSTEMS-BASED IMAGE-TEXT VISUALIZATION, FUSION AND MULTI-INTENT MODELS’ CONSTRUCTION pp. 1-15

Wang Meng, Suzan J. Obaiys, Yeliz Karaca and Nur Amalina Binti Jamaludin

PROXIMAL POLICY OPTIMIZATION FOR COLLISION AVOIDANCE AND MOTION PLANNING IN AUTONOMOUS VEHICLES: A MATHEMATICAL MODELING PERSPECTIVE pp. 1-15

Mohammad Hijji, Muhammad Munsif, Mohammed Alwakeel, Ahmed Alwakeel, Fahad Aradah, Faouzi Alaya Cheikh, Muhammad Sajjad and Khan Muhammad

STRUCTURAL DYNAMICS WITHIN THE EVOLUTION OF THE COMPLEX SYSTEMS THROUGH CHAOS PECULIARITIES WITH QUANTUM STATISTICAL PERSPECTIVE pp. 1-15

Ghulam Bary, Waqar Ahmed, Riaz Ahmad, A. B. Albidah, Wasif Ali, Juxiang Shao, Duohui Huang, Wei Sin Koh, Hala H. Taha and Ilyas Khan

CHARACTERIZATION OF COMPLEX STRUCTURES WITH CHAOTIC PHENOMENA AND DETERMINATION OF CHAOS IN STOCHASTIC COMPLEX SYSTEMS pp. 1-15

Ghulam Bary, Waqar Ahmed, Riaz Ahmad, Juxiang Shao, Duohui Huang, Mohsen Bakouri, Ilyas Khan and Wei Sin Koh

DYNAMIC RELATIONSHIP BETWEEN CARBON TRADING SYSTEM RESILIENCE AND LOW-CARBON STOCK MARKET RETURNS USING TIME-VARYING GRANGER CAUSALITY pp. 1-15

Qizhi He, Mati Ur Rahman, Jiawei Hu and Jinxin Cui

NEW BOUNDS FOR q-HADAMARD-TYPE INTEGRAL INEQUALITIES FOR GENERALIZED CONVEX FUNCTIONS WITH APPLICATION pp. 1-15

Humaira Kalsoom and Zareen A. Khan

ENTROPY GENERATION ANALYSIS OF DUSTY FLUID WITH PERISTALSIS IN ASYMMETRIC CHANNEL WITH SLIP EFFECTS pp. 1-11

Atifa Kanwal, Ambreen Afsar Khan, Aziz Khan, D. K. Almutairi and Thabet Abdeljawad

ON THE STABILITY ANALYSIS AND NUMERICAL DYNAMICS OF THE NONLINEAR BLACK–SCHOLES EQUATION IN CONFORMABLE ARISING IN ECONOMY pp. 1-11

Qiliang Chen, Asif Yokus, Haci Mehmet Baskonus and Wei Gao

ARTIFICIAL NEURAL NETWORK TECHNIQUE FOR SOLVING ONE-DIMENSIONAL FRACTIONAL RAYLEIGH–STOKES EQUATION pp. 1-11

Yones Esmaeelzade Aghdam, Hamid Mesgarani, Samira Bozorgi, Hossein Jafari and Nguyen van Thinh

BOUNDS FOR GENERALIZED FRACTIONAL INTEGRAL OPERATORS OF GENERALIZED STRONGLY CONVEX FUNCTIONS VIA MITTAG-LEFFLER FUNCTIONS pp. 1-11

Yonghong Liu, Ghulam Farid, Ferdous M. O. Tawfiq, Jongsuk Ro and Hafsa Yasmeen

INTELLIGENT COMPUTING PARADIGM FOR STOCHASTIC SIS MODEL WITH DOUBLE EPIDEMIC DISEASES pp. 1-27

Kottakkaran Sooppy Nisar, Muhammad Shoaib, Adeeba Haider, Maria and Muhammad Asif Zahoor Raja

ANALYZING THE DYNAMICS OF BREAST CANCER PROGRESSION WITH FRACTIONAL MODELING AND SIMULATION: EFFECTS OF ESTROGEN AND UNHEALTHY DIETS pp. 1-27

Tmader Alballa, Rahat Zarin, Aurang Zeb, Amir Khan, Hamiden Abd El-Wahed Khalifa and Usa Wannasingha Humphries

BREAST LESION SEGMENTATION AND CLASSIFICATION USING U-NET SALIENCY ESTIMATION AND EXPLAINABLE RESIDUAL CONVOLUTIONAL NEURAL NETWORK pp. 1-22

Mamuna Fatima, Muhammad Attique Khan, Saima Shaheen, Hussain Mobarak Albarakati, Shuihua Wang, Syeda Fizzah Jilani and Mohammad Shabaz

NUMERICAL SOLUTION OF A MULTI-TERM TIME-FRACTIONAL VISCOELASTIC NON-NEWTONIAN FLUID MODEL VIA A HYBRID SPECTRAL METHOD pp. 1-22

Kamran, Farman Ali Shah, Ibrahim Mahariq, Souhail Bouzgarrou, Salma Aljawi and J. F. Gã“mez-Aguilar

FRACTAL-INSPIRED SENTIMENT ANALYSIS: EVALUATION OF LARGE LANGUAGE MODELS AND DEEP LEARNING METHODS pp. 1-12

Hatoon S. Alsagri and Shahab Saquib Sohail

A COMPUTATIONAL ANALYSIS OF 𠒜ℬ𠒞 HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS OF TYPE II pp. 1-12

Asma, Yasra Khan, Sadique Ahmad, Abeer D. Algarni and Manel Hleili

A NOVEL NUMERICAL METHOD FOR SOLVING MODIFIED ATANGANA–BALEANU FRACTIONAL PROBLEMS BASED ON THE OPERATIONAL MATRIX METHOD pp. 1-12

Lana Abdelhaq, Sondos M. Syam and Muhammed I. Syam

SOME OSCILLATION RESULTS FOR TWO RIEMANN–LIOUVILLE FRACTIONAL DYNAMIC EQUATIONS ON TIME SCALES pp. 1-12

Qinghua Feng

OPTICAL SOLITON SOLUTION OF THE BENNEY–ROSKES ZAKHAROV–RUBENCHIK SYSTEMS pp. 1-12

Mehmet Fatä°h Uã‡ar

A COMPREHENSIVE ANALYSIS AND OPTIMAL CONTROL FOR A NONLINEAR (φ1,φ2)-FRACTIONAL DIFFERENTIAL EQUATIONS TOXIC DRINKS MODEL PERTAINING TO MITTAG-LEFFLER KERNEL TECHNIQUES pp. 1-31

Tahir Abbas, Saima Rashid, Yeliz Karaca and Yu-Ming Chu

EDITORIAL ARTICLE OF SPECIAL ISSUE: PART I-A SERIES — MATHEMATICAL MODELING OF COMPLEX SYSTEMS: FRACTALS-FRACTIONAL-ITÔ-DEs- WAVELET-ENTROPY-AI-BASED THEORIES, ANALYSES AND APPLICATIONS pp. 1-48

Yelä°z Karaca, Dumitru Baleanu, Yu-Dong Zhang, Osvaldo Gervasi and Majaz Moonis

DYNAMIC ANALYSIS AND HAMILTONIAN ENERGY ASPECTS OF HYPERCHAOTIC MEGASTABLE OSCILLATOR pp. 1-13

Gayathri Vivekanandhan, Karthikeyan Rajagopal, Anitha Karthikeyan, Salah Boulaaras and Asma Alharbi

BAYESIAN INFERENCE TO PREDICT NEXT LOWER RECORDS: AN APPLICATION IN EPIDEMIOLOGICAL MODELING pp. 1-13

Abbas Pak, Iman Makhdoom, Mohammadreza Mahmoudi and Amir Mosavi

A MATHEMATICAL MODEL FOR CONTROLLING THE ALCOHOL ADDICTION: STABILITY AND NUMERICAL ANALYSIS pp. 1-13

Samia Bushnaq, Anwar Zeb, Sidra Iqbal, Salih Djilali and Khursheed J. Ansari

APPLICATION OF A FRACTAL FRACTIONAL DERIVATIVE WITH A POWER-LAW KERNEL TO THE GLUCOSE–INSULIN INTERACTION SYSTEM BASED ON NEWTON’S INTERPOLATION POLYNOMIALS pp. 1-21

Muflih Alhazmi and Sayed Saber

SENSITIVITY ANALYSIS AND NUMERICAL MODELING OF INFLUENZA PROPAGATION AND INTERVENTION STRATEGIES UNDER THE FRACTAL-FRACTIONAL OPERATOR pp. 1-30

Rahat Zarin, Usa Wannasingha Humphries, Hamiden Abd El-Wahed Khalifa and Aeshah A. Raezah

ADVANCED DYNAMIC NUMERICAL SCHEME FOR FRACTAL-FRACTIONAL DIFFERENTIAL OPERATORS FOR CYTOTOXIC T LYMPHOCYTE MODEL PERTAINING TO MITTAG-LEFFLER KERNEL pp. 1-30

Tahir Abbas, Saima Rashid, Yeliz Karaca and Yu-Ming Chu

STABILITY ANALYSIS OF GDP-NATIONAL DEBT DYNAMICS USING DELAY DIFFERENTIAL EQUATION pp. 1-7

Qiliang Chen, Dipesh, Pankaj Kumar and Haci Mehmet Baskonus

A DELAYED MALWARE PROPAGATION MODEL FOR CLOUD COMPUTING SECURITY pp. 1-19

Xiaodong Yu and Zizhen Zhang

AN INTELLIGENT FRAMEWORK FOR HYBRID NANOFLUID FLOW BETWEEN TWO CONCENTRIC CYLINDERS BASED ON DEEP NEURAL NETWORKS pp. 1-20

Faiza, Waseem, Shazia Habib, Salah Boulaaras, Mati Ur Rahman, Sabir Ali and Asma Alharbi

THE TRIVIAL COUPLING APPROACH FOR THE WEAK ORDER USING THE MONTE CARLO METHOD WITH THE INVERTIBLE SCHEME pp. 1-9

Yousef Alnafisah

CODIMENSION TWO PHENOMENA OF A DELAY DIFFERENCE EQUATION pp. 1-9

Bo Li, Mohammadreza Mahmoudi and Zohreh Eskandari

MANEUVERING PENETRATION METHOD FOR MISSILE UNDER UNKNOWN INTERCEPTION STRATEGIES BASED ON TRANSFER DEEP REINFORCEMENT LEARNING pp. 1-14

Yaokun Wang, Pan Kai, Huatao Chen, Kun Zhao, Juan L. G. Guirao and Dengqing Cao

COMPUTATIONAL ALGORITHMS AND THERMAL DYNAMICS: ENGINEERING A SUSTAINABLE ENERGY FRAMEWORK pp. 1-14

Muhammad Ahsan, Amel Ali Alhussan, El-Sayed M. El-Kenawy and Namra Ashraf

TESTING FOR THE MULTIFRACTALITY IN AIR POLLUTANTS TIME SERIES AND APPLICATION TOÂ TABUK REGION CASE STUDY pp. 1-14

Abdulrahman F. Aljohani, Anouar Ben Mabrouk, Mounirah Areshi, Jamel Bouslimi, Ali H. Laatar and Abdallah A. Shaltout

SOME NEW INTEGRAL INEQUALITIES OF OSTROWSKI TYPE BY INCORPORATING THE ATANGANA–BALEANU FRACTIONAL INTEGRAL OPERATOR pp. 1-14

Humaira Kalsoom and Zareen A. Khan

IMPLEMENTING THREE-QUBIT GROVER’S ALGORITHM USING REAL QUANTUM PLATFORMS pp. 1-14

Marco Simonetti, Damiano Perri and Osvaldo Gervasi

FLIP BIFURCATION AND NUMERICAL STUDY OF CRIMEAN–CONGO HEMORRHAGIC FEVER WITH SUSTAINABLE FRACTIONAL APPROACH pp. 1-26

Aqeel Ahmad, Ali Raza, Muhammad Farman, AKGÃœL Ali, Muhammad Nauman Aslam, Dumitru Baleanu, Suhad Ali Osman Abdallah and N. S. Abd El-Gawaad

FRACTIONAL-ORDER MODEL OF IMMUNIZATION AND MULTIDRUG RESISTANCE IN PEOPLE WITH TUBERCULOSIS: LYAPUNOV STABILITY, MODELING AND CHAOS CONTROL pp. 1-26

Kottakkaran Sooppy Nisar, Muhammad Farman, Dumitru Baleanu, Saba Jamil, Changjin Xu, Ahmad O. Hourani and Aceng Sambas

Volume 34, issue 03, 2026

Erratum: PREDICTIVE MODELING OF REAL-TIME COLORECTAL CANCER VIA HYPERPARAMETER CONFIGURATION WITH DEEP LEARNING USING PUBLIC HEALTH INDICATOR ANALYSIS pp. 1-2

Jamal Alsamri, Fatima Quiam, Mashael Maashi, Abdullah M. Alashjaee, Mohammad Alamgeer and Ahmed S. Salama

FRACTAL STUDY OF BINGHAM FLUID FLOW IN DUAL POROUS MEDIA WITH ASYMMETRIC CHARACTERISTICS pp. 1-13

Jiaqing Hu, Shanshan Yang and Qian Zheng

STRENGTHENED VERSION OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR HARMONICALLY CONVEX FUNCTIONS BASED ON JENSEN–MERCER INEQUALITY pp. 1-13

Fangfang Shi, Muhammad Amir Ali, Wei Liu and Dongdong Gao

PARAMETERIZED INEQUALITIES INVOLVING MULTIPLICATIVE ψk-RAINA’S FRACTIONAL INTEGRALS pp. 1-39

Fuxiang Liu, Bingbing Fan and Jielan Li

EXPLORING THE PERTURBED FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION: APPLICATION IN THE OPTICAL FIBER AND QUANTUM MECHANICS pp. 1-17

Zi-Ge Wu and Kang-Le Wang

NUMERICAL APPROACH TO TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS USING EXTREME LEARNING MACHINE TECHNIQUE pp. 1-21

M. Fathima, S. Raja Balachandar, S. G. Venkatesh and H. Jafari

EXACT SOLUTIONS FOR THE FLOW OF TIME FRACTIONAL MODEL OF TERNARY NANOFLUID: APPLICATIONS IN CEMENTITIOUS MATERIALS pp. 1-18

Farhad Ali, Mishma Yousaf, Nadeem Ahmad Sheikh and Ilyas Khan

THE NONLINEAR MECHANISM OF INVESTORS’ BEHAVIOR AFFECTING THE MULTIFRACTALITY OF STOCK MARKET: EVIDENCE FROM CHINA pp. 1-18

Nan Xu, Songsong Li, Hao Xu and Weiqian Zhang

HERMITE–HADAMARD-TYPE INEQUALITIES VIA MULTIPLICATIVE FRACTIONAL CALCULUS AND APPLICATIONS TO SUPERQUADRATIC STRUCTURES pp. 1-29

Ghulam Jallani, Saad Ihsan Butt, Dawood Khan and Youngsoo Seol

VARIATIONAL PRINCIPLE, HAMILTONIAN, SENSITIVITY ANALYSIS AND NEW SOLITON SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER–HIROTA EQUATION pp. 1-16

Kui Liu and Kang-Le Wang

CONSTRUCTING SOLITON WAVE STRUCTURES FOR THE NONLINEAR FRACTIONAL COMPLEX GINZBURG–LANDAU EQUATION AND ITS STABILITY ANALYSIS USING AN ANALYTICAL APPROACH pp. 1-14

Mohammed S. Ghayad, Hamdy M. Ahmed, M. Elsaid Ramadan, Taher A. Nofal, Islam Samir and Karim K. Ahmed

DEVELOPING THE LIMIT-RESIDUAL FUNCTION METHOD FOR PROVIDING APPROXIMATE SOLUTIONS TO INITIAL AND BOUNDARY-VALUE PROBLEMS pp. 1-14

Ahmad El-Ajou

ADVANCED FRACTIONAL MODELING OF PHARMACOKINETIC PROCESSES USING mABC AND HILFER DERIVATIVES pp. 1-14

Merve Karaoglan, Erdal Bas and Salah Boulaaras

REMARKS ON THE RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF LIPSCHITZ FUNCTIONS pp. 1-9

S. T. Ding and Y. S. Liang

METRIC PROPERTIES FOR (−β)-TRANSFORMATION WITH NONRECURRENT ORBITS OF 1 pp. 1-9

Hui Hu and Xin Tong

ON MILNE-TYPE INEQUALITIES VIA KATUGAMPOLA FRACTIONAL MULTIPLICATIVE INTEGRALS pp. 1-22

Abdelghani Lakhdari, Bandar Bin-Mohsin, Khalid Achachera, Hongyan Xu and HÃœSEYIN Budak

STOCHASTIC EFFICIENCY OF WIND TIME SERIES IN NORTHEAST BRAZIL: A NOVEL APPROACH BASED ON INFORMATION-THEORY QUANTIFIERS pp. 1-20

Fã Bio Sandro Dos Santos, Fernando Henrique Antunes de Araujo, Alan de Queiroz Medeiros and Kerolly Kedma Felix Do Nascimento

COMPRESSION RATIO OF FRACTAL SETS pp. 1-19

Joel Ratsaby

THE FRACTAL CHARACTERISTICS OF THE FIBONACCI SEQUENCE pp. 1-5

H. R. Liang and Y. S. Liang

MATHEMATICAL MODELING AND ANALYSIS OF COVID-19 TRANSMISSION DYNAMICS VIA CAPUTO–FABRIZIO FRACTIONAL OPERATOR pp. 1-23

Gunaseelan Mani, Paramanathan Elangovan, John Paul Martin, Sabri T. M. Thabet, Imed Kedim and Thabet Abdeljawad

THE PROPERTY OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF THE LIPSCHITZ FUNCTION pp. 1-7

Y. Y. Yao

A CUSTOMIZED CLOSED-LOOP EEG-BASED INTERFACE SYSTEM TO ADJUST FOCUS, RELAXATION, AND ENGAGEMENT BY ALTERATION OF VISUAL STIMULI COMPLEXITY pp. 1-15

Mohammed Ali Salimi, Hamidreza Namazi and Reza Khosrowabadi

FRACTAL MULTI-SCALE PHYSICS-INFORMED NEURAL NETWORKS FOR FRACTAL-MODIFIED NONLINEAR OSCILLATORS pp. 1-15

Pinxia Wu, Zhiqiang Sheng and Chunhui He

CONSENSUS ANALYSIS OF WEIGHTED GENERALIZED WINDMILL NETWORKS: BASED ON CENTRAL NODE IMPORTANCE SHIFT pp. 1-11

Xiaoqian Wang, Qiuqiu Fan and Xin Chen

Volume 34, issue 02, 2026

ADVANCING FRACTIONAL BOUNDARY VALUE PROBLEMS SOLUTIONS USING SHIFTED VIETA–LUCAS POLYNOMIALS AND SPECTRAL APPROACHES pp. 1-17

Zulfiqar Ahmad Noor, Mohie M. Alqezweeni, Muhammad Bilal Riaz and Imran Talib

EXISTENCE, UNIQUENESS, HYERS–ULAM STABILITY AND CONTROLLABILITY RESULTS OF INTEGRO-DIFFERENTIAL EQUATIONS RELATED TO THE FRACTIONAL CAPUTO DERIVATIVE pp. 1-17

Govindaswamy Gokulvijay, Salah Boulaaras, Sriramulu Sabarinathan and Asma Alharbi

ANALYSIS OF HALL CURRENT EFFECTS ON UNSTEADY JEFFREY FLUID FLOW WITH FRACTIONAL MASS AND THERMAL TRANSPORT IN POROUS MEDIUM pp. 1-21

Imran Siddique, Laiba Ghafoor, Taha Radwan, Zaher Munder Yaseen and Barno Abdullaeva

NEW APPLICATIONS OF THE CAPUTO FRACTIONAL DERIVATIVE TO OBTAIN NUMERICAL SOLUTION OF THE COUPLED FRACTIONAL KORTEWEG–DE VRIES MODEL USING QUINTIC B-SPLINE FUNCTIONS pp. 1-21

Usama Ghafoor, Miguel Vivas-Cortez, Muhammad Abbas, Patricia J. Y. Wong, M. R. Alharthi, Y. S. Hamed and Muhammad Kashif Iqbal

INVESTIGATING THE SUCCESS OF IVF WITH FRACTIONAL-ORDER MODEL: ANALYSIS AND CASE STUDY pp. 1-21

Manal Ghannam, Bilgen Kaymakamzade, Muhammad Farman, Kottakkaran Sooppy Nisar, Fahad Aljuaydi and Aceng Sambas

SOLITARY WAVE STRUCTURES FOR TIME FRACTIONAL STOCHASTIC POISSON–NERNST–PLANCK MODEL IN ELECTROBIOCHEMICAL SYSTEM pp. 1-21

Muhammad Nadeem, Kalim U. Tariq, Rabia Khan, Kalim U. Tariq, Loredana Florentina Iambor, Mohamed Hussien and Mansour F. Yassen

ANALYSIS OF CAPUTO–FABRIZIO FRACTIONAL DERIVATIVE ON TUMOR-IMMUNE MATHEMATICAL MODEL WITH OPTIMAL CONTROL pp. 1-25

Shumaila Irum, Muhammad Asif, B. S. N. Murthy, M. N. Srinivas, A. S. Al-Moisheer, V. Madhusudanan and Anwar Zeb

THEORETICAL PREDICTIONS OF EXISTENCE AND UNIQUENESS FOR STOCHASTIC M-FRACTIONAL DIFFERENTIAL MODELS OF RANDOM BROWNIAN MOTION, EXHIBITED WITH MATRIX SPECTRAL COLLOCATION SOLUTIONS AND SIMULATED WITH THE ELECTRICAL ENGINEERING RLC UTILITY AS A CASE INTERPRETATION pp. 1-25

Haneen Badawi, Omar Abu Arqub and Raghad Eid

PREFACE: SPECIAL ISSUE ON “RECENT APPLICATIONS OF FRACTAL THEORY AND FRACTIONAL CALCULUS IN MATHEMATICAL PHYSICS†pp. 1-2

Omar Abu Arqub, Muhammad Nadeem and Yusuf Gurefe

NEW APPLICATIONS OF THE FRACTIONAL DERIVATIVES TO EXTRACT ABUNDANT SOLITON SOLUTIONS OF THE FRACTIONAL ESTEVEZ–MANSFIELD–CLARKSON EQUATION IN MATHEMATICAL PHYSICS pp. 1-13

Miguel Vivas-Cortez, Ghazala Akram, Maasoomah Sadaf, Saima Arshed, Muhammad Abbas, Qurrat-Ul-Ain and Y. S. Hamed

A COMPUTATIONAL APPROACH FOR ANALYZING THE APPROXIMATIVE TREATMENT OF FRACTIONAL-ORDERED DIFFUSION PROBLEMS pp. 1-13

Huaping Xiao, Jingmei Peng, Amra Al Kenany, Shaaban M. Shaaban and Hussam M. Gubara

INVESTIGATING JERK PHENOMENON BY USING FRACTAL-FRACTIONAL ANALYSIS pp. 1-13

Kamal Shah, Arshad Ali, Rohul Amin, Zeeshan Ali, Bahaaeldin Abdalla, Thabet Abdeljawad and Manar Alqudah

EXTENDED ANALYSIS ON RIEMANN–LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS: ANTI-PERIODIC BOUNDARY CONDITIONS OF VARIABLE ORDER pp. 1-13

Dean Chou, Mokhtari Mokhtar, Zoubida Bouazza, Mustafa Inc and Mohammed Said Souid

MEMORY EFFECTS IN THE GLYCOLYSIS PATHWAY: STABILITY, BIFURCATIONS, AND NUMERICAL SIMULATIONS pp. 1-13

Fatiha Mesdoui, Naziha Belmahi, Nabil Shawagfeh, Amirah Ayidh I Al-Thaqfan, Maha Ali, Haytham M. Rezk and Mohammed Zakarya

RADIOTHERAPY EFFECTS IN TUMOR TREATMENT: A PIECEWISE MODEL WITH DETERMINISTIC AND STOCHASTIC APPROACHES pp. 1-13

Salah Boulaaras, Seda Igret Araz and Asma Alharbi

APPLICATION OF FRACTAL-FRACTIONAL OPERATORS TO FRACTIONAL CHAOTIC SYSTEMS: INSIGHTS INTO COMPLEX DYNAMICS pp. 1-31

Muflih Alhazmi and Sayed Saber

USING NEURAL NETWORK AND FRACTALS FRACTIONAL ANALYSIS TO PREDICT THE EYE DISEASE INFECTION CAUSED BY CONJUNCTIVITIS VIRUS pp. 1-16

Kamal Shah, Khalil Ur Rehman, Bahaaeldin Abdalla, Thabet Abdeljawad and Wasfi Shatanawi

LOVE DYNAMICAL MODEL WITH PERSPECTIVES OF PIECEWISE DIFFERENTIAL OPERATORS pp. 1-24

Atul Kumar, Hambeer Singh, Sadique Ahmad and Ala Saleh Alluhaidan

SOLITON SOLUTIONS FOR THE HIGHER DIMENSIONAL FRACTIONAL CONFORMABLE STOCHASTIC MODIFIED KORTEWEG–DE VRIES–ZAKHAROV–KUZNETSOV MODEL pp. 1-18

Muhammad Nadeem, Kalim U. Tariq, Rabia Khan, A. I. Ismail, Mohamed Hussien and Khalid Suliman Aboodh

OPTIMAL CONTROL ANALYSIS OF A FRACTIONAL-ORDER MODEL FOR ONLINE GAMING ADDICTION pp. 1-12

Muhammad Nadeem, Mustafa Habib, Rifat Ansar, Shazia Karim, Loredana Florentina Iambor, Asma Abbas Hassan Elnour and Wedad M. Alawad

TWO-SCALE APPROACH FOR THE ANALYSIS OF TIME-FRACTIONAL DIFFUSION PROBLEMS IN HETEROGENEOUS MEDIA pp. 1-10

Jingmei Peng, Huaping Xiao, Asim Suleman A. Alwabel, Sharifah E. Alhazmi and Abdelaziz G. M. Musa

MODELING AND STABILITY ANALYSIS OF NEUROLOGICAL DISORDER UNDER ALZHEIMER’S DISEASE WITH NOVEL FRACTIONAL TECHNIQUE pp. 1-19

Ammara Talib, Muhammad Farman, Abdullahi Umar Ibrahim, Khadija Jamil, Kottakkaran Sooppy Nisar and Aceng Sambas

PSEUDOSPECTRAL FRACTIONAL DIFFERENTIATION MATRICES FOR SOLVING RICCATI AND BAGLEY–TORVIK FRACTIONAL MODELS VIA MIXED SHIFTED POLYNOMIALS pp. 1-15

Weam G. Alharbi, Dalal M. Almutairi, Dina Abdelhamied, Marwa M. Alzubaidi, Mounirah Areshi, M. El-Kady and M. Abdelhakem

THEORETICAL STUDY OF FRACTIONAL DIFFERENTIAL EQUATIONS UNDER UNCERTAINTY INVOLVING GENERAL MEMORY KERNELS pp. 1-15

Hossein Jafari, Muhammad Imran Liaqat, Yusif S. Gasimov and Nguyen van Thinh

AN INVERSE TIME-DEPENDENT DIFFUSION COEFFICIENT PROBLEM FOR A SPACE-FRACTIONAL DIFFUSION EQUATION pp. 1-11

Smina Djennadi, Omar Abu Arqub, Marwan Abukhaled and Nabil Shawagfeh

SOLUTIONS OF THE HYPERBOLIC FRACTIONAL INCLUSIONS UNDER WEAK ASSUMPTIONS IN BANACH SPACES pp. 1-11

Hossein Jafari, Meryem Meddahi, Nguyen van Thinh and Yusif S. Gasimov

ANALYTICAL ANALYSIS OF FRACTIONAL DAMPED BURGERS’ EQUATION USING CAPUTO DERIVATIVE IN FLUID AND PLASMA FIELDS pp. 1-11

Jinxing Liu, MUREÅžAN Sorin, Ebraheem Alzahrani, Mohamed Hussien and Sabir Widatalla

Volume 34, issue 01, 2026

EXPLORING THE FRACTIONAL WAVE PROFILES TO THE GENERALIZED TRUNCATED BOGOYAVLENSKY–KONOPELCHENKO EQUATION pp. 1-18

Jan Muhammad, Usman Younas and Ahmed Zubair Jan

AI-POWERED PHYSICS-CONSTRAINED TRANSFORMER FRAMEWORK: A NEW APPROACH TO SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS pp. 1-18

Xuejuan Li, Qi Li and Wenjing Zhao

ON THE COMPLEX DYNAMICS OF SIMPLE INTEGER TO FRACTIONAL-ORDER SINE CHAOTIC OSCILLATORS pp. 1-18

Bei Gao, Ali Shukur, Muhammad Marwan and Ning Wang

VISIBILITY OF NON-SELF-SIMILAR SETS pp. 1-6

Yi Cai and Yang Yang

DYNAMICS OF THE NEW EXACT WAVE SOLUTIONS TO THE LOCAL FRACTIONAL VAKHNENKO–PARKES EQUATION pp. 1-6

Yan-Hong Liang and Kang-Jia Wang

MAGNETIZATION CURRENT AND MAGNETIC SUSCEPTIBILITY FROM PAULI EQUATION IN THE CONTEXT OF CONFORMABLE FRACTIONAL DERIVATIVE pp. 1-12

Ilyas Haouam

FRACTAL DIMENSION OF SUBSTITUTION TREE NETWORKS pp. 1-12

Qingcheng Zeng, Yumei Xue, Daohua Wang and Ying Miao

FINITE-TIME STABILITY OF FRACTIONAL-ORDER NEURAL NETWORKS WITH PROPORTIONAL DELAY pp. 1-10

Yanrong An, Muhammad Aamir Ali, Jarunee Soontharanon and Thanin Sitthiwirattham

A COMPREHENSIVE STUDY ON THE VARIATIONAL FORMULATION OF THE FRACTAL-FRACTIONAL KDV-ZK EQUATION WITH VISCOELASTICITY INSIGHTS AND APPLICATIONS pp. 1-10

Yan Wang, Lizhong Chen and Zhongxi Liu

UNVEILING DIVERSE EXACT SOLUTIONS AND FRACTIONAL-ORDER EFFECTS IN THE MODIFIED KORTEWEG–DE VRIES EQUATION VIA THE EXP-FUNCTION METHOD pp. 1-10

Weifan Hou, Na Qie, Jihuan He, Jinfeng Ma, Meigeng Gao, Zhou Chen and Chunhui He

EXPLORING AND PREDICTING THE NONLINEAR DYNAMICS OF ISLAMIC FIXED-INCOME SECURITIES BY GENERALIZED CHAOS ANALYSIS AND WAVELET NEURAL NETWORKS pp. 1-35

Markus Vogl, Milena Kojiä†, Petar Mitiä†, Aida Haniä† and Fernando Henrique Antunes de Araujo

MULTIPLICATIVE (k,p)-HADAMARD FRACTIONAL INTEGRALS WITH APPLICATIONS TO MERCER-TYPE INEQUALITIES pp. 1-35

Ziyi Zhou, Xianbao Yuan and Tingsong Du

GENERALIZED BOOLE’S TYPE INEQUALITIES ON FRACTAL DOMAINS: FRACTAL FRACTIONAL APPROACH AND APPLICATIONS pp. 1-31

Saad Ihsan Butt, Muhammad Mehtab and Youngsoo Seol

MULTIFRACTAL ANALYSIS OF CONSUMER BEHAVIOR DURING COVID-19 pp. 1-13

Okyu Kwon and Gabjin Oh

FRACTAL IMAGE CODING WITH DEEP IMAGE PRIOR AND TOTAL VARIATION REGULARIZATION FOR SALT-AND-PEPPERS NOISE REMOVAL pp. 1-13

Chuling Wen, Weijie Liang, Jian Lu, Chen Xu and Yuru Zou

THE ANALYSIS OF A FRACTIONAL ORDER REACTION–DIFFUSION SYSTEM USING VARIATIONAL ITERATION METHOD pp. 1-13

Gauhar Ali, Noor Khan and Yong Wang

APPLICATION OF A NOVEL VARIABLE-ORDER FRACTIONAL NEUTRON POINT KINETICS MODEL FOR NUCLEAR REACTOR REACTIVITY TRANSIENT ANALYSIS pp. 1-17

F. A. Godã Nez, S. Quezada-Garcã A, G. Fernã Ndez-Anaya, L. A. Quezada-Tã‰llez and M. A. Polo-Labarrios

EARLY DETECTION OF FUNGAL DISEASES IN MANGO LEAVES: FUSION OF GLCM FEATURES AND VISION TRANSFORMERS WITH DEEP NEURAL NETWORK CLASSIFICATION pp. 1-17

Juliã N Patiã‘o Ortiz, Ricardo Carreã‘o Aguilera, Sergio Juã Rez Vã Zquez, Miguel Patiã‘o Ortiz and Marã A Angã‰lica Chã Vez Benã Tez

MATHEMATICAL MODELING OF PSYCHOLOGICAL DISEASE BY USING ARTIFICIAL INTELLIGENCE TOOLS pp. 1-21

Manar A. Alqudah, Kamal Shah, Fatemah Mofarreh and Thabet Abdeljawad

HERMITE–HADAMARD-TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR MULTIPLICATIVELY (h,m)-PREINVEX INTERVAL-VALUED FUNCTIONS pp. 1-23

Yun Tan, Dafang Zhao and Guoshan Deng

AVOIDING INTERSECTIONS OF DRAGON CURVES pp. 1-23

Reimund Albers, Zongyi Guo and Huaiyi Guo

A FRACTAL PERMEABILITY MODEL FOR THE DISK-SHAPED BIFURCATION NETWORK WITH TORTUOSITY EFFECT CONSIDERING THE INFLUENCE OF SURFACE ROUGHNESS pp. 1-11

Yi Li, Boqi Xiao, Lei Chen, Yifan Gong, Yu Yang, Yongjun Xiao, An Feng and Yi Wang

ANALYTICAL APPROXIMATION TO THE DISTRIBUTION OF BREAKDOWN COEFFICIENTS FOR BINARY BETA-LOGNORMAL DISCRETE MULTIFRACTAL CASCADES pp. 1-11

Andreas Langousis, Alin A. Carsteanu and Roberto Deidda

BIFURCATING LUMP SOLITON STRUCTURES IN THE FRACTIONAL DRINFEL’D SOKOLOV WILSON FRAMEWORK pp. 1-15

Naveed Iqbal, Shah Hussain, Wael W. Mohammed, Yousef Jawarneh, Akbar Ali and Taher S. Hassan

DIVERSITY OF SOLITON SOLUTIONS TO THE NONLINEAR FRACTIONAL KADOMA EQUATION pp. 1-15

Kang-Le Wang

A REVIEW OF FRACTAL EEG ANALYSIS IN NEUROLOGICAL AND PSYCHIATRIC DISORDERS pp. 1-14

Najmeh Pakniyat, Huma Khan and Hamidreza Namazi

RESISTANCE DISTANCES IN SKELETON NETWORKS OF SIERPINSKI HEXAGON pp. 1-14

Jiaqi Fan, Zenghui Fang and Keman Hu

APPROXIMATION BY THE HÖLDER CONTINUOUS FUNCTIONS WITH THE SAME FRACTAL DIMENSION pp. 1-9

B. Q. Wang and Y. S. Liang

ENERGY-CONSERVING NUMERICAL SCHEME FOR SPACE-FRACTIONAL DAMPED NONLINEAR SCHRÖDINGER EQUATIONS pp. 1-20

Ying Wang, Yongqi Yang and Yue Shen

EXPLORING THE β-FRACTIONAL TELEGRAPH EQUATION: INVESTIGATING THE OPTICAL SOLITARY WAVES, INTERACTION SOLUTIONS AND MULTISTABILITY ANALYSIS pp. 1-22

Usman Younas, Jan Muhammad, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah and Imtiaz Ahmad