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Adaptation of kernel functions-based approach with ABC distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations
  • omar abu arqub,
  • Jagdev Singh,
  • Mohammed Alhodaly
omar abu arqub
Al Balqa Applied University
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Jagdev Singh
JECRC University
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Mohammed Alhodaly
King Abdulaziz University
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Abstract

Mathematical modeling of uncertain FIDEs is an extremely significant topic in electric circuits, signal processing, electromagnetics, and anomalous diffusion systems. Based on the RKA, a touching numerical approach is considering in this study to solve groups of FFIDEs with ABC fractional distributed order derivatives. The solution-based approach ‎lies in generating infinite orthogonal basis from kernel functions, where 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 A(D) and B(D). 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 indicating by employing several experiments. From theoretical viewpoints, the acquired results signalize that the utilize 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.

Peer review status:ACCEPTED

25 Oct 2020Submitted to Mathematical Methods in the Applied Sciences
26 Oct 2020Submission Checks Completed
26 Oct 2020Assigned to Editor
05 Nov 2020Reviewer(s) Assigned
12 Dec 2020Review(s) Completed, Editorial Evaluation Pending
14 Dec 2020Editorial Decision: Revise Minor
20 Dec 20201st Revision Received
21 Dec 2020Submission Checks Completed
21 Dec 2020Assigned to Editor
21 Dec 2020Reviewer(s) Assigned
21 Dec 2020Review(s) Completed, Editorial Evaluation Pending
26 Dec 2020Editorial Decision: Accept