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The aim of this paper is to investigate the existence of anti-periodic solutions for a nonlinear coupled system of [Formula omitted]Caputo fractional differential equations with [Formula omitted]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 [Formula omitted]Caputo fractional calculus paired with measures of noncompactness. As an application, our theoretical results have been illustrated by providing an interesting example., Author(s): Ali El Mfadel [sup.1] [sup.2], Said Melliani [sup.2], M'hamed Elomari [sup.2] Author Affiliations: (1) https://ror.org/02m8tb249, grid.460100.3, 0000 0004 0451 2935, Superior School of Technology, Sultan Moulay Slimane University, , [...]

The main crux of this manuscript is to establish the existence and uniqueness of solutions for nonlocal fractional evolution equations involving ψ−Caputo fractional derivatives of an arbitrary order α ∈ (0, 1) with nondense domain. The mild solutions of our proposed model are constructed by employing generalized ψ−Laplace transform and some new density functions. The proofs are based on Krasnoselskii fixed point theorem and some basic techniques of ψ−fractional calculus. As application, a nontrivial example is given to illustrate our theoritical results.

In this paper, we have applied a new method called Laplace Residual Power Series Method (LRPSM) introduced by Eriqate et al. for solving the fuzzy non-homogeneous wave equation. The algorithm gains powerful results for this kind of problem. Initially, we analyze in general the Laplace residual power series technique, and then we expand it and use it to solve the fuzzy non-homogeneous wave equation with the extended Hukuhara differentiability. [ABSTRACT FROM AUTHOR]

The purpose of the present work is investigating a degenerate parabolic equation with anisotropic p-Laplacian operator and strongly nonlinear source under boundary conditions of Dirichlet type; the existence of a periodic non-negative solution is shown. The proof is based on the Leray–Schauder topological degree, which is tricky to work with in this kind of equations. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the existence, uniqueness and stability of solutions for some nonlocal impulsive evolution problems involving conformable fractional derivative. The main results are based on fixed point theorems combined with the semigroup theory. As applications, we give an example to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

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]

Fuzzy fractional pantograph stochastic differential equations (FFPSDEs) is investigated here. The initial objective is to show the existence and uniqueness of solutions using Banach fixed point theorem. The second objective is discussing averaging principle of FFPSDEs, precisely, we will prove that the solutions of FFPSDEs can be approximated in the sense of mean square by the solutions of averaged fuzzy fractional stochastic system. [ABSTRACT FROM AUTHOR]

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]

This paper aims to introduce the new concept of an α-θ-Geraghty type contraction mapping using CG-simulation in a metric-like space. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. We provide some examples as an application that proves the credibility of our results. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the problem \begin{eqnarray*}\begin{cases} u^{(\alpha)}(t)=Au(t)+f(t,u(t))& t\in [0,T]\\ u(0)=u_0, D^{\alpha}u(0)=u_1\end{cases}\end{eqnarray*} \begin{eqnarray*} \begin{cases} u^{(\alpha)}(t)=Au(t)+f(t,u(t))& t\in [0,T]\\ u(0)=u_0, D^{\alpha}u(0)=u_1 \end{cases} \label{pb1} \end{eqnarray*} Where $\alpha\in (1,2]$, and we use the conformable derivative. We give the notion of $\alpha$-Cosine families and proveded the existence and uniqueness of the problem 0.1.

In this paper, we use an intuitionistic fuzzy Laplace transforms for solving intuitionistic fuzzy hyperbolic equations precisely the transport equation with intuitionistic fuzzy data under strongly generalized H-differentiability concept. For this purpose, the intuitionistic fuzzy transport equation is converted to the intuitionistic fuzzy boundary value problem (IFBVP) based on the intuitionistic fuzzy laplace transform. The related theorems and properties are proved in detail. Finally, we solve an example to illustrate this method.

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]

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]

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]

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 establish some new generalized results on the equivalence of K -functionals and modulus of continuity of functions defined on the Sobolev space L α , β 2 ℝ , by using the harmonic analysis related to the Jacobi-Dunkl operator Δ α , β , where α ≥ β ≥ − 1 / 2 and α ≠ − 1 / 2. [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]

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions. [ABSTRACT FROM AUTHOR]

In the present work, we establish the existence and uniqueness result of the linear heat equation with Conform derivative in Colombeau generalized algebra. We using for the first time the notion of a generalized conformable semigroup and the purpose of introducing Conform derivative is regularizing it in Colombeau. [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]

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]