Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications

Mohammed Al-Smadi, Omar Abu Arqub and Dia Zeidan

Chaos, Solitons & Fractals, 2021, vol. 146, issue C

Abstract: In this manuscript, we introduced, analyzed, and studied fuzzy fractional differential equations in terms of Atangana-Baleanu-Caputo differential operator equipped with uncertain constraints coefficients and initial conditions. To this end, we discussed both the fuzzy Atangana-Baleanu-Caputo fractional derivative and integral. Also, Newton-Leibniz fuzzy inversion formulas for both derivative and integral are proved. Using Banach fixed point theorem, existence and uniqueness results of solution are established by means of fuzzy strongly generalized differentiability of fuzzy fractional differential equation with Atangana-Baleanu fractional derivative under the Lipschitz condition. To achieve the above results, some prerequisite provisions for characterizing the solution in synonymous systems of crisp Atangana-Baleanu-Caputo fractional differential equations are argued. In this tendency, a new computational algorithm is proposed to obtain analytic solutions of the studied equations. To grasp the debated approach, some illustrative examples are provided and analyzed by the figures to visualize and support the theoretical results.

Keywords: Fuzzy ABC fractional derivative; Fuzzy AB fractional integral; Fuzzy ABC FDE; Characterization theorem; Fuzzy ABC SGD; Fuzzy ABC solution (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002447

DOI: 10.1016/j.chaos.2021.110891

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