the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales r...

Abstract. The problem of synchronization between non-identical hyperchaotic fractional order systems is discussed in this article. We use the method of active control to synchronize the chaotic trajectories. To illustrate the proposed theory, we consider two particular examples of synchronization in fractional order hyperchaotic systems viz. Rossler system with new system and Chen system with L...

This paper deals with the feedback control of a DC motor speed with using the fractional-order controller. The permanentmagnet DC motor is often used in mechatronic and other fields of control theory and therefore its control is very important. The mathematical description of the fractional order controller and its implementation in the analogue and the discrete domains is presented. An example...

‎In this article‎, ‎the multi-step conformable fractional differential transform method (MSCDTM) is applied to give approximate solutions of the conformable fractional-order differential systems‎. ‎Moreover‎, ‎we check the stability of conformable fractional-order L\"{u} system with the MSCDTM to demonstrate the efficiency and effectiveness of the proposed procedure.

This paper deals with synchronization between a fractional order Coullet chaotic system and an integer order Rabinovich-Fabrikant chaotic system by using tracking control and stability theory of fractional order system. An effective controller is designed to synchronize these two systems. Numerical simulations have been done by using Mathematica and Matlab both. Numerical solutions via Grünwald...

In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name „state“ space for the integer-order and fractional-order system and the importance of the initialization function for the fractionalorder system. Some implications concernin...

Based on the traditional IS–LM economic theory, which shows the relationship between interest rates and output in the goods and services market and the money market in macroeconomic. We established a four-dimensional IS–LM model involving four variables. With the Caputo fractional calculus theory, we improved it into a fractional order nonlinear model, analyzed the complexity and stability of t...

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

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...