A COMPUTATIONAL ANALYSIS FRACTIONAL COMPLEX-ORDER VALUES BY ABC OPERATOR AND MITTAG-LEFFLER KERNEL MODELING

Mohammed A. El-Shorbagy, Mati Ur Rahman and Yelä°z Karaca
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Mohammed A. El-Shorbagy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Â Al-Kharj 11942, Saudi Arabia2Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt
Mati Ur Rahman: School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, P. R. China4Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Yelä°z Karaca: University of Massachusetts Chan Medical School (UMASS), 55 Lake Avenue North, Worcester, MA 01655, USA6Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge, MA 02139, USA

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-19

Abstract: A random arbitrary-order mathematical system is investigated via the global and non-singular kernel of Atangana–Baleanu in the sense of Caputo (𠒜ℬ𠒞) derivative in this study where the proposed problem is divided into four general compartments for the explanation. To show the existing result, the Krasnosilkii’s theorem from the theory of fixed points is used, whereas the well-known Banach theorem is utilized in order to show that the solution is unique to the proposed problem. Furthermore, by using the idea of Hyers–Ulam (UH) stability, the generalized problem is perturbed little for the purpose of checking its stability. The numerical solution is evaluated by applying the Adams–Bashforth iterative techniques. The numerical examples derived are tested in order to illustrate the established outcomes along with the numerical simulation to demonstrate the verification of the results obtained. The dynamics of every compartment is examined on different non-integer order 𠒷 and by choosing arbitrary time t by the taken approximate solution employing the AB numerical technique. Ultimately, the total continuous spectrum on the dynamics of each quantity in any arbitrary order lying between any of the two natural values, namely 0 and 1, has been achieved based on the investigated analyses.

Keywords: Fractional General Problems; Adams–Bashforth Iterative Technique; Existence and Unique Solution; Krasnosilkii’s Theorem and Banach Contraction; Krasnoselskii’s Fixed Point Theorem; Mittag-Leffler Kernel; Hyers–Ulam Stability; Fixed Point Theorem; Arbitrary-order Mathematical Models; Global and Non-singular Kernel; Fractional Differential Equations; Fractional Complex-order Values; Computational Fractional Analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401643

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