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The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish…
The motive behind this manuscript is to set up the existence and uniqueness of a positive solution for a fractional thermostat model for certain values of the parameter $\lambda>0$. We accomplish sufficient conditions for the existence of a…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…
This paper studies a nonlinear fractional implicit differential equation (FIDE) with boundary conditions involving a HilferHadamard type fractional derivative. We establish the equivalence between the Cauchy-type problem (FIDE) and its…
The present research paper is devoted to investigate the existence, uniqueness of mild solutions for impulsive delay integrodifferential equations with integral impulses in Banach spaces. We also investigate the dependence of solutions on…
In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\]…
Utilising the notion of measures of non-compactness and Kamke function of order $\alpha$, we address the question of solvability of fractional differential equations in Banach spaces. In particular, we provide sufficient conditions ensuring…
This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…
Picard's iteration has been used to prove the existence and uniqueness of the solution for stochastic integral equations, here we use Schauder's fixed point theorem to give a new existence theorem about the solution of a stochastic integral…
This paper is concerned with the qualitative properties of the solutions of mixed integro-differential equation \begin{equation}\label{eq 1} \left\{ \arraycolsep=1pt \begin{array}{lll} (-\Delta)_x^{\alpha} u+(-\Delta)_y u+u=f(u)\quad \ \…
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is…
The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate on the solutions, the continuous dependence of the solutions on initial conditions as well as the existence and uniqueness of…
Investigating the existence, uniqueness, stability, continuous dependence of data among other properties of solutions of fractional differential equations, has been the object of study by an important range of researchers in the scientific…
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…
This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition. We use the equivalent integral equation to study the considered Hilfer differential problem with…
This paper is concerned with a class of nonlinear boundary value problem involving fractional derivative in the $\varphi$-Riemann-Liouville sense. Some Properties of the Green's function for this problem are mentioned. By means of the…
In this paper, we investigate a class of stochastic impulsive fractional differential evolution equations with infinite delay in Banach space. Firstly sufficient conditions of the existence and uniqueness of the mild solution for this type…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…