In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...

Necessary and sufficient stability instability conditions are reviewed extended for multi-term homogeneous linear fractional differential equations with Caputo derivatives constant coefficients. A comprehensive review of the state art regarding analysis two-term three-term fractional-order is provided, which then to case four-term equations. The properties characterized respect coefficients equ...

Necessary and sufficient conditions are explored for the asymptotic stability instability of linear two-dimensional autonomous systems fractional-order differential equations with Caputo derivatives. Fractional-order-dependent fractional-order-independent properties fully characterized, in terms main diagonal elements systems' matrix, as well its determinant.

In the Present manuscript we have investigate the Adaptive projective synchronization between different fractional order chaotic systemsusing modified adaptive control method with unknown parameters. The modified adaptive control method is very affective and more convenient in compression to the existing method for the synchronization of the fractional order chaotic systems. The chaotic attract...

In this paper, we consider a fractional model of telegraph equation in terms of voltage and current. The fractional derivatives are taken in the Caputo sense. The numerical algorithm based on the homotopy perturbation transform method (HPTM) is applied to obtain analytic and approximate solutions of the space-time fractional telegraph equations. The HPTM is combined in the form of Laplace trans...

Abstract: In this paper, we study the approximation of analytical solution for Fractional Reaction Diffusion model which describes the evaluation of bacterium Bacillus, which grows on the surface of thin agar plates, by using homotopy analysis transform method. The fractional derivatives are described by caputo sense. A comparative study between the homotopy analysis transform method and the cl...

Noether theorems for two fractional singular systems are discussed. One system involves mixed integer and Caputo derivatives, the other only derivatives. Firstly, primary constraints constrained Hamilton equations given. Then, of established, including identities, quasi-identities conserved quantities. Finally, results obtained illustrated by examples.