in this paper we present a new method for solving fractional optimal control problems with delays in state and control. this method is based upon bernstein polynomial basis and using feedback control. the main advantage of using feedback or closed-loop controls is that they can monitor their effect on the system and modify the output accordingly. in this work, we use bernstein polynomials to tr...

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, ·} and L = G(q, p)∂q + F (q, p)∂p, which are used in equations of motion, are derivative operators. We consider fractional derivatives on a set of classical observables as fractional powers of derivative operators. As ...

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

There is a debate among contemporary mathematicians about what it really means by a fractional derivative. The question arose as a consequence of introducing a ‘new’ definition of a fractional derivative. In a reply Ortigueira and Machado [1] came up with several very important criteria to determine whether a given derivative is a fractional derivative. According to their criterion, the new fra...

The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...