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This article considers the fuzzy nonlinear neutral Caputo-Nabla difference equation of order 0

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]

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]

In this paper, we establish some new existence results for certain coupled systems of nonlinear Ψ-fractional differential equations with four-point fractional integral boundary conditions. The proofs are derived from Banach fixed point theorem. As an application, a nontrivial example is presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This manuscript aims to highlight the existence and uniqueness results for the following Schrödinger problem in the extended Colombeau algebra of generalized functions. 1 / ı ∂ / ∂ t u t , x − △ u t , x + v x u t , x = 0 , t ∈ R + , x ∈ R n , v x = δ x , u 0 , x = δ x , where δ is the Dirac distribution. The proofs of our main results are based on the Gronwall inequality and regularization method. We conclude our article by establishing the association concept of solutions. [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]