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In this paper, we introduce a novel theorem concerning the existence of solutions for Coupled Systems of Time-Fractional Differential Problems. This is achieved through the utilization of the ψ-Caputo fractional derivative, where the order is confined within the range of 0 < α < 1. The validation of the existence result is demonstrated by employing certain conditions, namely Lipschitz and Carathéodory conditions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the existence of anti-periodic solutions for a nonlinear coupled system of Ψ - Caputo fractional differential equations with p - Laplacian operator in a Banach space. The proofs of our main results are based on Mönch's fixed point theorem and some basic tools of Ψ - Caputo fractional calculus paired with measures of noncompactness. As an application, our theoretical results have been illustrated by providing an interesting example. [ABSTRACT FROM AUTHOR]

In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov's direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]