this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

In this article we have considered Fredholm integro-differential equation type second-order boundary value problems and proposed a rational difference method for numerical solution of the problems. The composite trapezoidal quadrature and non-standard difference method are used to convert Fredholm integro-differential equation into a system of equations. The numerical results in experiment on s...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

Pricing American options using partial (integro-)differential equation based methods leads to linear complementarity problems (LCPs). The numerical solution of these problems resulting from the Black-Scholes model, Kou’s jumpdiffusion model, and Heston’s stochastic volatility model are considered. The finite difference discretization is described. The solutions of the discrete LCPs are approxim...

Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...

In this study, we develop a theory for the nonlocal hybrid boundary value problem fractional integro-differential equations featuring Atangana–Baleanu derivatives. The corresponding integral equation is presented. Then, establish existence results using Dhage’s fixed point theorem sum of three operators. We also offer additional exceptional cases and similar outcomes. order to demonstrate verif...

We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integr...