In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.

a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...

In this article the problem of an interface fracture between two isotropic linear elastic materials is studied within a continuum modeling framework, which incorporates important nanoscale effects. The proposed model of bi-material crack ascribes curvature-dependent surface tension to both the fracture surfaces and the solid-solid interface. Further, it uses as boundary conditions the jump mome...

This paper is concerned with a technique for solving Fredholm integro-dierentialequations in the reproducing kernel Hilbert space. In contrast with the conventionalreproducing kernel method, the Gram-Schmidt process is omitted hereand satisfactory results are obtained. The analytical solution is represented inthe form of series. An iterative method is given to obtain the approximate solution.Th...

The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

The Tau method, produces approximate polynomial solution of differential, integral and integro-differential equations (see [E.l,Ortiz, The Tau method, SIAM J. Numer. Anal. 6 (3) (1969) 480–492; E.l. Ortiz, H. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing 27 (1981) 15–25; S.M. Hosseini, S. Shahmorad, A matrix formulat...