Fuzzy Fractional Evolution Equations and Fuzzy Solution Operators

Abstract

In this paper, the fuzzy fractional evolution equations of order q (FFEE) with fuzzy Caputo fractional derivative are introduced. We study the existence and uniqueness of mild solutions for FFEE under some conditions. Also, we generalize the definition of the fuzzy fractional integral and derivative order q. The fuzzy Laplace transform is presented and proved. The solvability of the problem (FFEE) and the properties of the fuzzy solution operator and its generator are investigated and developed.

Fuzzy Generalized Conformable Fractional Derivative

“…For further research we propose the study for fuzzy fractional differential equations, by using the generalized conformable differentiability concept. In addition, we propose to extend the results of the present paper and to combine them with the results in [15] for fuzzy fractional differential equations.…”

Existence, Uniqueness and Approximate Solutions of Fuzzy Fractional Differential Equations

“…In Section 2 we recall some basic results on fuzzy number. In Section 3 we introduce some basic results on the conformable fractional differentiability [4,5] and conformable integrability [5,6] for the fuzzy set-valued mapping in [7]. In Section 4 we show the relation between a solution and its approximate solution to the Cauchy problem of the fuzzy fractional differential equation, and furthermore, and we prove the existence and uniqueness theorem for a solution to the Cauchy problem of the fuzzy fractional differential equation.…”

Fuzzy Conformable Fractional Semigroups of Operators

“…e concept of fuzzy fractional derivative was introduced by [15] and developed by [16][17][18][19], but these researchers tried to put a definition of a fuzzy fractional derivative. Most of them used an integral from the fuzzy fractional derivative.…”

“…Recently, Harir et al [20] defined a new well-behaved simple fractional derivative called "the fuzzy conformable fractional derivative" depending just on the basic limit definition of the derivative. ey proved the product rule and the fractional mean value theorem and solved some (conformable) fractional differential equations [18].…”