n this paper, we study the existence and uniqueness of an intuitionistic fuzzy solution for semi-linear integro-differential equations with non-local conditions using Banach fixed point theorem. Theorem on these problems nonlocal are presented under certain assumptions. Finally, example is established to illustrate effectiveness

In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

in previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. then we extendedthis research to the simulation of continuous fuzzy systems models. in this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. consider a crisp continuous system whose evolution depends ondifferential equations. such a ...

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these modeled with Integro-Differential Equations (IDEs); generalizations differential equations comprise both and component. For example, brain not accurately by since their b...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

In the present study, we investigate the symmetry groups of Benney equations that are the system of nonlinear integro-differential equations. We first investigate the symmetry groups of the Benney equations by using the method. Then we obtain all reduced forms of the system of integro-differential equations with fewer variables based on symmetry groups; and lastly, we seek a similarity solution...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...

We consider nonlinear integro-differential equations like the ones that arise from stochastic control problems with purely jump Lévy processes. We obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior C 1; ̨ regularity for general fully nonlinear integro-differential equations. Our estimates remain uniform as the degree of the equation approaches 2, so they can be seen ...