FRACTAL INTEGRAL INEQUALITIES FOR GENERALIZED HARMONICALLY CONVEX FUNCTIONS USING LOCAL FRACTIONAL INTEGRALS AND RAINA’S MAPPING WITH RELATED APPLICATIONS

Lei Chen (), Taha Radwan (), Ahsan Fareed Shah, Miguel Vivas-Cortez and Muhammad Shoaib Saleem
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Lei Chen: General Education Department, Anhui Xinhua University, Hefei 230088, P. R. China
Taha Radwan: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
Ahsan Fareed Shah: Faculty of Mathematics, FGEID, (C/G), MoD, Pakistan4Department of Mathematics, University of Okara, Okara, Pakistan
Miguel Vivas-Cortez: Facultad de Ciencias Exactas, Naturales y Ambientales Exactas Pontificia Universidad Católica del Ecuador, Sede Quito, Ecuador
Muhammad Shoaib Saleem: Department of Mathematics, University of Okara, Okara, Pakistan6Center for Theoretical Physics, Khazar University, Baku, Azerbaijan

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-16

Abstract: Fractional calculus has proved its worth in engineering and as well as in medicine, analyzing papilloma-virus infection, typhoid fever, myelogenous leukemia, monkeypox, dengue infection, hand–foot–mouth disease, zika virus, and lymphatic filariasis infection. Fractal sets famous for their complex geometric features have gained remarkable attention in the last few decades due to their applications in image processing, data compression, and signal analysis. Our work merges fractional calculus, fractal sets, convexity and integral inequalities to get a broader perspective of this area of research. The main goal of this study is to introduce a new notation for harmonically convex mappings (ℋ𠒞ℱs) called generalized ℧-exponential type ℋ𠒞ℱs over fractal space settings using Raina’s mapping. Various fractional variants of Hermite–Hadamard-type inequalities (ℋℋ℠s) for this novel generalization cover the main section of this research. The graphical representations of the main results empower their validity. Finally, connecting findings with applications and the classical Mittag-Leffler mapping makes the study more enjoyable.

Keywords: Raina’s Mapping; Fractal Set; Generalized Harmonically ℧-Exponential-Type Convex Mapping; Hermite–Hadamard-Type Inequality; Local Fractional Integrals Mittag-Leffler Mapping (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401504

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