Abstract: In this paper, Laplace decomposition method is developed to solve linear and nonlinear fractional integrodifferential equations. The proposed method is based on the application of Laplace transform to nonlinear fractional integro-differential equation. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivative is described in the Caputo se...

We develop a general construction for nonlinear Lévy processes with given characteristics. More precisely, given a set Θ of Lévy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical Lévy processes with triplets in Θ. The nonli...

A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order k k ≥ 2 for the sequence of iterates is also established. It is found that the w...

This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the ...

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 ...

In this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integro-differential equation arising in the field of fluid mechanics is investigated. First, an equivalency lemma is presented by which the problem understudy is converted to the two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions...

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...

This paper presents the application of the Homotopy Analysis Method (HAM) as a numerical solution to linear integro-differential equation. The HAM contains the auxiliary parameter , taht provides a powerful tool to analyze strongly linear and nonlinear problems. Examples are provided to demonstrate the advantages of HAM over the homotopy perturbation method (HPM), sine-cosine wavelets and CAS w...