# Approximate Solution of Integro-differential Equations System

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In this paper, we establish the existence and uniqueness of mild and classical solutions of quasilinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition in Banach space. The results are established by using the semigroup theory and Banach fixed point theorem.

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In this paper, the LU-representation of fuzzy number is considered and based on the LUrepresentation of fuzzy volterra integro-differential equation (FVIDE) is discussed. The existence of solution of FVIDE is brought in details. Then, the solution is found in three cases of FVIDE that is...

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In this work, we propose the Shannon wavelets approximation for the numerical solution of a class of integro-differential equations which describe the charged particle motion for certain configurations of oscillating magnetic fields. We show that using the Galerkin method and the connection...

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In this paper, we first establish the existence theorem of travelling wave solutions in an integro-difference competition system by Schauder's fixed-point theorem, the cross-iteration and the upper and lower solutions method. To illustrate our result, we present an application to an...

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In this paper, reproducing kernel Hilbert space method is applied to approximate the solution of two-point boundary value problems for fourth-order Fredholm-Volterra integrodifferential equations. The analytical solution was calculated in the form of convergent series in the space W52[a, b] with...