Abstract Terminal value problems of fractional linear systems with non-homegenous terms are investigated in this paper for the first time. They equivalent to a second kind weakly singular Volterra–Fredholm integral system. Picard’s method is used obtain closed form solution. The exact solution checked satisfy terminal problem. Numerical solutions provided comparison truncated ones.

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...

In recent years many integral inequalities for continuous and discontinuous functions have been established, which provide handy tools for investigating the quantitative and qualitative properties of solutions of integral and differential equations [1-17]. In the investigations for integral inequalities, the idea of generalizing known integral inequalities have gained extensive attention. In [1...

A numerical method based on modified block pulse functions is proposed for solving the mixed linear Volterra-Fredholm integral equations. We obtain an integration operational matrix of interval [0,T). and their integration, equations can be reduced to a system algebraic The rate convergence O(h) error analysis are discussed. Some examples provided show that have good degree accuracy.

Abstract We solve the closed range problem for Volterra-type integral operator on Fock spaces. Several applications of result related to operators invertibility, Fredholm, and dynamical sampling structures from frame perspectives are provided. further prove a bounded preserves no property. On contrary, adjoint if only it is noncompact but fails preserve both tight frames Riesz basis.

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...