adomian decomposition method has been applied to solve many functional equations so far. in this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. we interpret a fuzzy differential equation by using the strongly generalized differentiability. also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

Correlation functions of exactly solvable models can be described by differential equations [1]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations. We derive an integro-differential equation, which describes time and temperature dependent correlation function 〈ψ(0, 0)ψ(x, t)〉T of penetrable Bose gas. The integrodif...

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...

This work studies various types of input/output representations for analytic input/output operators. It is shown that if an operator satisfies an integro-differential input/output equation or an integral one, then it is locally realizable by analytic state space systems. This generalizes the results previously obtained for differential input/output equations to integral and integro-differential...

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

In this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated to verify convergence results and to illustrate the efficiently of the method.