Related papers: On the $\varepsilon$-regular mild solution for fra…
The motivation that the field of differential equations provide to several researchers for the challenges that have been challenging them over the decades has contributed to the strengthening of the area within mathematics. In this sense,…
The aim of this work is to investigate the conditions for the existence and continuation of a mild solution to the initial value problem of functional-differential equations of neutral type in Banach spaces to the boundary of the domain.…
The artefact is dedicated towards the inspection of nonlinear fractional differential systems involving Riemann-Liouville derivative with higher order and fixed lower limit, including non-instantaneous impulses for existence and uniqueness…
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…
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…
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…
In this paper, we are concerned with the mild solutions of Riemann-Liouville fractional differential equations with nonlocal conditions in Banach space. We use Banach contraction principle to prove the existence and uniqueness. Moreover, we…
We provide a convenient framework for the study of the well-posedness of a variety of abstract (integro)differential equations in general Banach function spaces. It allows us to extend and complement the known theory on the maximal…
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 study some properties of $\psi$-Hilfer fractional integrodifferential equations. We obtain the existence and uniqueness and other properties such as continuous dependence of solution. The tools used for obtaining our result…
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…
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…
In this paper, we study the existence and uniqueness of pseudo $S$-asymptotically $\omega$-periodic mild solutions of class $r$ for fractional integro-differential neutral equations. An example is presented to illustrate the application of…
We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded…
In this paper, we present a new class of inequality of the Gronwall type and discuss some particular cases. In this sense, we investigate the uniqueness and $\delta$-Ulam-Hyers-Rassias stability of the mild solution for the fractional…
In this paper, we investigate the existence of mild solutions to Hilfer fractional equation of semi-linear evolution with non-instantaneous impulses, using the concepts of equicontinuous $C_{0}$-semigroup and Kuratowski measure of…
Since the main work on Ulam-Hyers dependable stabilities of differential equations to date, numerous significant and applicable papers have been published, both in the sense of integer order and fractional order differential equations.…
In this paper, we investigate the existence and uniqueness of $(\omega,{\rho})$-periodic solutions for a class of the abstract impulsive integro-differential equations on Banach space.
This paper analyses a Kirchhoff type quasilinear space-time fractional integro-differential equation with memory $(\mathcal{K}^{s}_{\alpha})$. Various a priori bounds are derived in different norms on the solution of the considered…
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…