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In this paper, we study the existence result of solutions for fuzzy nonlinear fractional differential equations involving Caputo differentiability of an arbitrary order 0 < q < 1. As application, an example is included to show the applicability of our result. [ABSTRACT FROM AUTHOR]

The main crux of this work is to study the existence of solutions for a certain type of nonlinear Ψ-Caputo fractional differential equations with anti-periodic boundary conditions and p-Laplacian operator. The proofs are based on the Leray–Schauder degree theory and some basic concepts of Ψ-Caputo fractional calculus. As an application, our theoretical result has been illustrated by providing a suitable example. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence, uniqueness, and finite-time stability results for fractional delayed Newton cooling-law equation involving ψ-Caputo fractional derivatives of order α ∈ (0,1). By using Banach fixed point theorem, Henry-Gronwall type retarded integral inequalities, and some techniques of ψ-Caputo fractional calculus, we establish the existence and uniqueness of solutions for our proposed model. Based on the heat transfer model, a new criterion for finite time stability and some estimated results of solutions with time delay are derived. In addition, we give some specific examples with graphs and numerical experiments to illustrate the obtained results. More importantly, the comparison of model predictions versus experimental data, classical model, and non-delayed model shows the effectiveness of our proposed model with a reasonable precision. [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 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]

In this paper, we present the new extension of Colombeau algebra of generalized functions construct by Mirjana Stojanovic. After we proved the existence and uniqueness of Cauchy problems with fractional derivatives in the Colombeau algebra. [ABSTRACT FROM AUTHOR]