Fractional differential equations with Atangana–Baleanu fractional derivative: Analysis and applications

Existence results for hybrid fractional differential equations with Hilfer fractional derivative

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

Fractional differential equations with Legendre polynomials

Applications of Fractional Differential Equations

By considering different definitions of fractional derevatives, we study some kind of fractional differential equations and also give some of there applications.

Differential equations with fractional derivative and universal map with memory

Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann–Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their present state is determined by all past states with special forms of weights. To obtain discrete maps from fractional differential equations, we use the equival...

Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...