EXISTENCE AND UNIQUENESS RESULTS FOR FUZZY BOUNDARY VALUE PROBLEMS OF NONLINEAR DIFFERENTIAL EQUATIONS INVOLVING ATANGANA-BALEANU FRACTIONAL DERIVATIVES

EXISTENCE AND UNIQUENESS RESULTS FOR FUZZY BOUNDARY VALUE PROBLEMS OF NONLINEAR DIFFERENTIAL EQUATIONS INVOLVING ATANGANA-BALEANU FRACTIONAL DERIVATIVES

F. Zamtain, M. Elomari, S. Melliani, A. EL Mfadel

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Abstract

This manuscript is devoted to the investigation of the existence and uniqueness results for fuzzy fractional boundary value problems of some nonlinear di erential equations in- volving fuzzy Atangana-Baleanu fractional derivatives of order   2 (1; 2). By applying Banach  xed point theorem, some new results and properties of Atangana-Baleanu fractional derivatives and generalized Hukuhara di erence, we establish our main existence theorems. As application, a nontrivial example is given to illustrate our theoretical results.

Keywords

fuzzy number, fuzzy fractional integral, fuzzy Atangana-Baleanu derivative, fuzzy Fractional di erential equations, Banach  xed point theorem.