We investigate a class of fractional neutral evolution equations on Banach spaces involving Caputo derivatives. Main results establish conditions for the controllability fractional-order system and existence solution to an optimal control problem minimum energy. The are proved with help fixed-point semigroup theories.

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.

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...

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration meth...

A parallel numerical simulation algorithm is presented for fractionalorder systems involving Caputo-type derivatives, based on the AdamsBashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using several different approaches: a pure MPI version, a combination of MPI with OpenMP optimization and a memory saving speedup approach. All tests run on a BlueGene/P c...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system...

This paper proposed a fractional model for the flow rate and characteristic of the impurity of order α, β(0<α, β≤1) respectively, which describes one dimensional dynamical flows of electrically conducting fluid. In this model fractional derivatives are described in the Caputo sense. The beauty of the paper is residual analysis which shows that our approximate solution converges very rapidly to ...

This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the...

and Applied Analysis 3 Definition 2 (see [3]). The Caputo fractional derivative of order q > 0 with the lower limit zero for a function u is defined as C D q t u (t) = 1 Γ (n − q) ∫ t 0 (t − s) n−q−1 u (n) (s) ds, t > 0, 0 ≤ n − 1 < q < n, (8) where the function u(t) has absolutely continuous derivatives up to order n − 1. If u is an abstract function with values in E, then the integrals which ...