In this paper we study numerical methods for hybrid fuzzy fractional differential equation, Degree of Sub element hood and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition.

It is well known that fractional differential equations appeared more and more frequently in different research areas, such as fluid mechanics, viscoelasticity, biology, physics, engineering and other areas of science [1-30]. Considerable attention have been spent in recent years to develop techniques to look for solutions of nonlinear fractional partial differential equations (NFPDEs). Consequ...

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein–Gordon equation can be used as numerical algorit...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach (Fractional Calculus and Applied Analysis, ...

The diffusion equation is related to the Schrödinger equation by analytic continuation. The formula E2=p2c2 + m2c4 leads to a relativistic Schrödinger equation, and analytic continuation yields a relativistic diffusion equation that involves fractional calculus. This paper develops stochastic models for relativistic diffusion and equivalent differential equations with no fractional derivatives....

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo’s fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp.

Keywords: Analytic semigroup Banach fixed point theorem Caputo derivative Faedo–Galerkin approximations Nonlocal conditions Neutral fractional differential equation a b s t r a c t This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H. We study an associated integral equation...