Related papers: Properties of Some $\psi$-Hilfer fractional Integr…
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
This paper deals with the existence and uniqueness of solutions for a nonlinear boundary value problem involving a sequential $\psi$-Hilfer fractional integro-differential equations with nonlocal boundary conditions. The existence and…
In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and {\delta}-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $\psi$-Hilfer fractional derivative.…
In this paper, we investigate the existence and uniqueness of solution of nonlinear $\psi$-Caputo fractional differential equation with the help of Banach fixed point theorem. Moreover, by using $\psi$-Gronwall inequality, we studied some…
The aim of this paper is to obtain the existence of unique solution to nonlinear Cauchy-type problem. We consider the implicit nonlinear Cauchy-type problem with $\psi$-Hilfer fractional derivative. The Banach fixed point theorem is used to…
In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam--Hyers--Rassias stability of the non-instantaneous impulsive integrodifferential equation by means of $\psi$-Hilfer fractional derivative. In this…
This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $\varphi$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the…
This paper is committed to establishing the assumptions essential for the existence and uniqueness results of a fractional functional integrodifferential equation (FFIDE) having a derivative of generalized Hilfer type. Using the Picard…
We prove, using a fixed point theorem in a Banach algebra, an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result…
In this paper, we initially derive the equivalent fractional integral equation to $\Psi$-Hilfer hybrid fractional differential equations and through it, we prove the existence of a solution in the weighted space. The primary objective of…
We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the $\psi$-Hilfer fractional derivative. In addition, we discuss the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of its solutions. A few examples…
By means of the recent $\psi$-Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rassias on closed intervals $[a,b]$ and $[a,\infty)$ for a…
In this paper, using the Riemann-Liouville fractional integral with respect to another function and the $\psi-$Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro-differential…
In this paper we introduce a new fractional derivative with respect to another function the so-called $\psi$-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we…
In this paper, we consider the nonlinear $\Psi$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $\Psi$--Hilfer fractional differential equations with time delay. It is…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
We introduce a new version of $\psi$-Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated and, in particular, we prove an integration by parts formula. Using the Laplace…