This manuscript is devoted to the investigation of the existence results of fractional Cauchy problem for some nonlinear ψ−Caputo fractional dierential equations with non local conditions. By applying xed point theorems, some results of topological degree theory for condensing maps and some fractional analysis techniques, we establish some new existence theorems. As application, a nontrivial example is given to illustrate our theoretical results.

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In this paper we will try to give sense to the notion of intuitionistic fuzzy α-semigroups. Our objective is to solve an intuitionistic fuzzy evolution (differential equation) problem. Since the concept of linear operators is not defined on the set of all intuitionistic fuzzy numbers, we found an obvious inspiration from the nonlinear evolution problem in the classical case.

In this manuscript, we are concerned with the existence result of nonlinear hybrid differential equations involving ψ−Caputo fractional derivatives of an arbitrary order α ∈ (0, 1). By applying Krasnoselskii fixed point theorem and some fractional analysis techniques, we prove our main result. As application, a nontrivial example is given to demonstrate the effectiveness of our theoretical result.

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.