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

被引:83
作者
Al-Smadi, Mohammed [1 ,2 ]
Abu Arqub, Omar [3 ,4 ]
Zeidan, Dia [5 ]
机构
[1] Al Balqa Appl Univ, Ajloun Coll, Dept Appl Sci, Ajloun 26816, Jordan
[2] Ajman Univ, Nonlinear Dynam Res Ctr NDRC, Ajman, U Arab Emirates
[3] Al Balqa Appl Univ, Fac Sci, Dept Math, Salt 19117, Jordan
[4] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia
[5] German Jordanian Univ, Sch Basic Sci & Humanities, Amman, Jordan
关键词
Fuzzy ABC fractional derivative; Fuzzy AB fractional integral; Fuzzy ABC FDE; Characterization theorem; Fuzzy ABC SGD; Fuzzy ABC solution; PARTIAL INTEGRODIFFERENTIAL EQUATIONS; HILBERT-SPACE METHOD; NUMERICAL-SOLUTIONS; 2-PHASE FLOW; MODEL;
D O I
10.1016/j.chaos.2021.110891
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
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页数:14
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