This article introduces a numerical method based on an M(n+ 1) set of general, hybrid orthonormal Bernstein functions coupled with Block-Pulse Functions(HOBB) on the interval [0,1] for approximating solutions of a Coupled System of linear and non linear Volterra integral and Integro-Differential equations. This method reduces a Coupled System of Volterra integral and IntegroDifferential equatio...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

This paper is concerned with the controllability results of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion infinite delay in real separable Hilbert space. The are obtained using analysis, theory resolvent operator sense Grimmer and Krasnoselskii fixed point theorem. An example provided to illustrate theory.

In this paper, by employing the fixed point theory and the monotone iterative technique, we investigate the existence of a unique solution for a class of nonlinear fractional integrodifferential equations on semi-infinite domains in a Banach space. An explicit iterative sequence for approximating the solution of the boundary value problem is derived. An error estimate is also given. © 2013 Else...

−∞ x(s) dsR(t, s) = 0 the existence of nonoscillatory solutions is studied. A general comparison theorem is obtained which allows to compare oscillation properties of equations with concentrated delays to integrodifferential equations. Sharp nonoscillation conditions are deduced for some autonomous integrodifferential equations. Using comparison theorems, an example is constructedwhere oscillat...

We introduce a one parameter family of non-linear, non-local integrodifferential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of th...

In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and nonlinear memory source term. For 1, will be considered on bounded domain ℝ d . By some Sobolev embeddings properties Mittag-Leffler function, give results existence uniqueness mild solution (1.1) below. When = introduce L p −...