Abstract
In this manuscript, we establish new existence and uniqueness results for fuzzy linear and semilinear fractional evolution equations involving Caputo fractional derivative. The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. As application, we conclude this paper by giving an illustrative example to demonstrate the applicability of the obtained results.
Highlights
Fuzzy fractional calculus and fuzzy fractional differential equations are a natural way to model dynamical systems subject to uncertainties
Arshad and Lupulescu in [10] proved some results on the existence and uniqueness of solution for the fuzzy fractional differential equations under Hukuhara fractional Riemann-Liouville differentiability
For many basic works related to the theory of fractional differential equations and fuzzy fractional differential equations, we refer the readers to the articles [15,16,17,18,19,20] and references therein
Summary
Fuzzy fractional calculus and fuzzy fractional differential equations are a natural way to model dynamical systems subject to uncertainties. In the past few years, many works have been done by several authors in the theory of fuzzy fractional differential equations (see [1,2,3]) This theory has been proposed to handle uncertainty due to incomplete information that appears in many mathematical or computer models of some deterministic real-world phenomena. In order to get a perfect model with a precise initial condition, Agarwal et al in [9] proposed the concept of solutions for fuzzy fractional differential equations. Motivated by the above works, in the present paper, we study the existence result of solution for the following fuzzy linear fractional evolution equation:.
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