Abstract This article discusses the stability results for solution of a fractional q -integro-differential problem via integral conditions. Utilizing Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on obtained, conditions are provided to ensure generalized Ulam Ulam–Hyers–Rassias stabilities original system. The illustrated by two examples.

In this paper, we study a new approach of investigation existence, uniqueness and stability the periodic solution nonlinear fractional integro-differential equation type Caputo-Fabrizio derivative with initial condition, boundary conditions, integral conditions by using successive approximations method Banach fixed point theorem. Finally, some examples are present to illustrate theorems.

In this paper, we consider a singularly perturbed integro-differential equation with rapidly oscillating right-hand side, which includes an integral operator slowly varying kernel. Earlier, differential and equations coefficients were considered. The main goal of work is to generalize the Lomov's regularization method identify side asymptotics solution original problem.

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) the first kind with spectral collocation method. proposed VO-LFDIDEs have multiterms integer, fractional-order derivatives dela...

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science engineering. Nonlocal boundary conditions more effective, some cases necessary, because they accurate measurements of the true state than classical (local) initial conditions. Closed-form solutions always desirable, not only efficient, but also can be valuable benchmarks...

Abstract This paper is devoted to the study of existence and multiplicity weak solutions a Hamiltonian integro-differential system. The main tool used theory min–max based on Mountain-Pass theorem. considered system Fredholm type imposed Dirichlet boundary conditions are occurred at integral bounds. Furthermore, we demonstrate some cases in which equivalent with classical

In this paper, we consider systems of singularly perturbed integro-differential equations with a rapidly oscillating right-hand side, including an integral operator slowly varying kernel. Differential type and inhomogeneity coefficient at unknown function are studied. The main goal work is to generalize the Lomov’s regularization method reveal influence side on asymptotics solution original pro...

In this paper, we study the existence of solution to integro-differential equations in space Lebesgue-integrable on un-bounded interval after transformed nonlinear integral functional equation, used tool is fixed point theorem due Schauder with weak measure non compactness, De-Blasi. addition, give an example which satisfies conditions our theorem.