in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

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.

In this paper, we simulate a maize streak virus (MSV) epidemic model using the Caputo-Fabrizio fractional derivative. We solve nonlinear fractional-order of MSV recently proposed efficient numerical method. perform several graphical simulations to explore dynamics. The investigations justify usefulness scheme in epidemiology. type generalization and implementation method are key features study.

In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grünwald–Letnikov derivative, the Riemann–Liouville derivative and the Caputo derivative. Especially, we compare the Riemann–Liouville derivative with the Caputo derivative. And sequential property of the Caputo derivative is also derived, which is helpful in translating the higher fractional-order di...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...