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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 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]

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.

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]

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]