Journal
CHAOS SOLITONS & FRACTALS
Volume 146, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2021.110891
Keywords
Fuzzy ABC fractional derivative; Fuzzy AB fractional integral; Fuzzy ABC FDE; Characterization theorem; Fuzzy ABC SGD; Fuzzy ABC solution
Categories
Funding
- Al-Balqa Applied University
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This manuscript presents the fuzzy fractional differential equations using the Atangana-Baleanu-Caputo differential operator with uncertain constraints coefficients and initial conditions. The existence and uniqueness results of solution are established using Banach fixed point theorem. A new computational algorithm is proposed to obtain analytic solutions, which are supported by illustrative examples and figures.
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 AtanganaBaleanu 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. (c) 2021 Elsevier Ltd. All rights reserved.
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