In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

In this paper, a multi-step differential transform method (MsDTM) is performed to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as amodel for HIV infection of CD4 T cells. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of fractiona...

In this article, Multi-step Differential Transform Method (MsDTM) extends to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as a Newton-Leipnik chaotic systems. The solutions of numerical obtained from proposed method reveal that the approach is very effective and convenient when apzplied to systems of fractional differential ...

Necessary and sufficient stability instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives constant coefficients. In both cases, fractional-order-dependent as well fractional-order-independent characterisations of properties obtained, in terms the coefficients equation. The theoretical results exemplified particular c...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

Chaos synchronization of coupled fractional order differential equation is receiving increasing attention because of its potential applications in secure communications and control processing. The aim of this paper is synchronization between two identical or different delay fractional-order chaotic systems in finite time. At first, the predictor-corrector method is used to obtain the solutions ...

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...