in this paper we intend to offer new numerical methods to solve the second-order fuzzy abel-volterraintegro-differential equations under the generalized $h$-differentiability. the existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

We consider the Cauchy problem on the positive half-line for the differential-delay equation ü(t) + 2c0(t)u̇(t) + c1(t)u̇(t − h) + d0(t)u(t) + d1(t)u(t − h) + d2(t)u(t − 2h) = 0 where ck(t), dj(t) (t ≥ 0; k = 0, 1; j = 0, 1, 2) are continuous functions. Conditions providing the positivity of the Green function and a lower bound for that function are derived. Our results are new even in the case o...

In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...

In this paper, we consider a new class of fuzzy functions called Fuzzy Integro- Differential Equations. Some numerical methods, such as Euler, have been used to determine the solutions these equations. We extend techniques find optimal by using control parameters, extended difference Euler technique is for this. Based on parametric form number, Equation divided into two systems second kind. Ill...

We investigate the relationship between discrete and continuous time in dynamic physical systems. Employing the common-sense picture behind derivatives, differential equations are translated into discrete-time analogues. The properties of qualitative simulation in discrete time are discussed. It is flirthennore shown that discrete time can be embedded in continuous time in a natural way without...

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions integro-sum inequalities; impulse integral inequalities . Some applications of the results are included: conditions of boundedness uniformly , stability by Lyapunov uniformly , practical stability by Chetaev uniformly for the solutions of impulsive differential and integrodifferential ...

in this paper, we consider first-order fuzzy differential equations with initial value conditions. the convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized h-differentiability, are studied. then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...