We consider a fractional program with both linear and quadratic equation in numerator and denominator  having second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a  second order cone programming (SOCP)  problem.  For the quadratic fractional case, using a relaxation, the problem is reduced to a semi-definite optimization (SDO) program. The p...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

In this paper, we consider the variable-order nonlinear fractional diffusion equation ∂u(x, t) ∂t = B(x, t)xR u(x, t) + f(u, x, t), where xR α(x,t) is a generalized Riesz fractional derivative of variable order α(x, t) (1 < α(x, t) ≤ 2) and the nonlinear reaction term f(u, x, t) satisfies the Lipschitz condition |f(u1, x, t) − f(u2, x, t)| ≤ L|u1 − u2|. A new explicit finite difference approxim...

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...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

Recently, interest in fractional-order inductors (FOIs) has increased since they allow for accurate and robust models of dynamical systems to be designed. However, practical implementation these not been possible due the lack single FOI realizations. To address this challenge, work, we propose a simple-to-realize inductor design with variable constant phase angle (CPA). The relies on characteri...

This paper is concerned with behavior analysis and improvement of wind turbines with Doubly Fed Induction Generator (DFIG) when using a new fractional-order control strategy during wind variations. A doubly fed induction generator, two types of variable frequency power electronic converters and two input wind waveforms are considered. A fractional-order control strategy is proposed for the wind...

It is known that the well-posedness of time-fractional reaction–diffusion models with Mittag-Leffler kernel usually requires non-physical constraints on initial data. In this paper, we propose a variable-order equation and prove aforementioned could be eliminated by imposing integer limit variable fractional order at time, which mathematically demonstrates physically-relevance modifications.

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...