Adaptation of kernel functions‐based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 7; pp. 7807 - 7834
• Main Authors: Abu Arqub, Omar, Singh, Jagdev, Alhodaly, Mohammed
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 15.05.2023
• Subjects: Algorithms; Atangana–Baleanu fractional integral; Atangana–Baleanu–Caputo fractional derivative; Circuits; Derivatives; Fractional calculus; fuzzy fractional integrodifferential equations; fuzzy inductance–resistance–capacitance circuit; Hilbert space; Integrals; Kernel functions; reproducing kernel algorithm
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.7228

Mathematical modeling of uncertain fractional integrodifferentials (FIDEs) is an extremely significant topic in electric circuits, signal processing, electromagnetics, and anomalous diffusion systems. Based on the reproducing kernel algorithm (RKA), a touching numerical approach is considering in this study to solve groups of fuzzy fractional integrodifferentials (FFIDEs) with Atangana–Baleanu–Caputo (ABC) fractional distributed order derivatives. The solution‐based approach lies in generating infinite orthogonal basis from kernel functions, where an uncertain condition is fulfilled. Thereafter, an orthonormal basis is erected to figurate fuzzy ABC solutions with series shape in idioms of η‐cut extrapolation in Hilbert space AD and BD. In this orientation, fuzzy ABC fractional integral, fuzzy ABC fractional derivative, and fuzzy ABC FIDE are utilized and comprised. The competency and accuracy of the suggested approach are indicated by employing several experiments. From theoretical viewpoints, the acquired results signalize that the utilization approach has several merits in feasibility and opportunity for treating with many fractional ABC distributed order models. In the end, highlights and future suggested research work are eluded.