Infinite horizon backward stochastic Volterra integral equations (BSVIEs for short) are investigated. We prove the existence and uniqueness of adapted M-solution in a weighted $L^2$-space. Furthermore, we extend some important known results finite BSVIEs to infinite setting. provide variation constant formula class linear duality principle between (forward) equation (SVIE an BSVIE As applicatio...

In this paper, we study the dividend payments prior to absolute ruin in a Markov-dependent risk process in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of integrodifferential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin...

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

We formulate and prove a non-local “maximum principle for semicontinuous functions” in the setting of fully nonlinear and degenerate elliptic integro-partial differential equations with integro operators of second order. Similar results have been used implicitly by several researchers to obtain comparison/uniqueness results for integro-partial differential equations, but proofs have so far been...

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differe...

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the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

Abstract: The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential...