Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators

Seda İĞRET Araz

Chaos, Solitons & Fractals, 2020, vol. 130, issue C

Abstract: In this paper, we suggest a new integro-differential equation by utilizing from the concept of fractal-fractional derivative and integral newly introduced by Atangana. We offer that under which conditions the solution of the suggested equation is exist and unique benefitting from Banach fixed-point theorem. Also, we construct a new numerical scheme for the numerical solution of our problem and we give numerical simulation and illustrations for different values of fractional order α and fractal order β. That’s why, this study will guide for researchers significantly in theory and applications.

Keywords: Fractal-fractional derivative; Fractal-fractional integral; Fractional integro-differential equation; New numerical scheme (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303315

DOI: 10.1016/j.chaos.2019.109396

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