Weighted Cauchy-type problem of a functional differ-integral equation

In this work, we are concerned with a nonlinear weighted Cauchy type problem of a differ-integral equation of fractional order. We will prove some local and global existence theorems for this problem, also we will study the uniqueness and stability of its solution

Coupled system of a fractional order differential equations with weighted initial conditions

Here, a coupled system of nonlinear weighted Cauchy-type problem of a diffre-integral equations of fractional order will be considered. We study the existence of at least one integrable solution of this system by using Schauder fixed point Theorem. The continuous dependence of the uniqueness of the solution is proved

On the stability of some fractional-order non-autonomous systems

The fractional calculus (integration and differentiation of fractional-order) is a one of the singular integral and integro-differential operators. In this work a class of fractionalorder non-autonomous systems will be considered. The stability (and some other properties concerning the existence and uniqueness) of the solution will be proved

Existence of a bounded variation solution of a nonlinear integral equation in L1(R+)

In this paper we study the existence of a unique solution of a nonlinear integral equation in the space of bounded variation on an unbounded interval by using measure of noncompactness and Darbo fixed point theorem

On the solvability of a functional Volterra integral equation

In this article, we will investigate the existence of a unique bounded variation solution for a functional integral equation of Volterra type in the space L1(R+) of Lebesgue integrable functions

On the existence of a bounded variation solution of a fractional integral equation in L1[0, T] due to the spread of COVID 19

In this article, we will investigate the existence and uniqueness of a bounded variation solution for a fractional integral equation in the space L1[0, T] of Lebesgue integrable functions

Global Existence for an Implicit Hybrid Differential Equation of Arbitrary Orders with a Delay

In this paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville fractional derivative with delay and its corresponding integral equation. Under some sufficient conditions, we establish the global and local existence results for that problem by applying some fixed point theorems. In addition, we have investigated the continuous and integrable solutions for that problem. Moreover, we discuss the continuous dependence of the solution on the delay function and on some data. Finally, further results and particular cases are presented

Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion

In this article, we consider a Riemann–Liouville fractional-order nonlinear hybrid delay differential inclusion with a nonlinear set-valued nonlocal integral condition of fractional order. We prove some existence and uniqueness results in C(I,R). We also study the continuous dependence of the solutions on the two sets of selections of the two set-valued functions, considered in our problem, and on some other parameters. Finally, to validate our results, we present an example and some particular cases

Global Existence for an Implicit Hybrid Differential Equation of Arbitrary Orders with a Delay

In this paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville fractional derivative with delay and its corresponding integral equation. Under some sufficient conditions, we establish the global and local existence results for that problem by applying some fixed point theorems. In addition, we have investigated the continuous and integrable solutions for that problem. Moreover, we discuss the continuous dependence of the solution on the delay function and on some data. Finally, further results and particular cases are presented