In this paper, we investigate the numerical study of nonlinear Fredholm integro-differential equation with fractional Caputo-Fabrizio derivative. We use Hermite wavelets and collocation technique to approximate exact solution by reducing a algebraic system. Furthermore, apply method on certain examples check its accuracy validity.

The main intention of the present research study is focused on analysis a Caputo fractional integro-differential boundary problem (CFBVP) in which right-hand side supposed differential equation represented as sum two nonlinear terms. Under integro-derivative conditions, we extract an equivalent integral and then define new operators based it. With help three distinct fixed-point theorems attrib...

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes s...

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of order integration and use it to solve integro-di?erential equations. The is described illustrated with examples. Also, we give error analysis.

In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.

In this paper, we study the existence of solutions for a new problem hybrid differential
 equations with nonlocal integro multi point boundary conditions by using proportional fractional
 derivative. The presented results are obtained fixed theorems three Dhage
 operators. application theoretical conclusions is demonstrated through an example.

In this paper, existence/uniqueness of solutions and approximate controllability concept for Caputo type stochastic fractional integro-differential equations (SFIDE) in a Hilbert space with noninstantaneous impulsive effect are studied. addition, we study different types iterative learning control SFIDEs impulses spaces. Finally, examples given to support the obtained results.

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...