in this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. the governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by sherief et al. [1] are considered as a special case. it is found that three types of...

Abstract: The object of this study is to develop a self-tuning fractional order proportionalintegral-derivative (SFOPID) controller for controlling the mover position of a direct drive linear voice coil motor (VCM) accurately under different operational conditions. The fractional order proportional-integral-derivative (FOPID) controller can improve the control performances of the conventional i...

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), adve...

A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space d...

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative o...

Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of fractional dynamic systems, this paper proposes a scale-dependent finite difference method (S-FDM) in which the non-uniform mesh depends on the time fractional deriva...

in this paper, inverse laplace transform method is applied to analytical solution of the fractional sturm-liouville problems. the method introduces a powerful tool for solving the eigenvalues of the fractional sturm-liouville problems. the results  how that the simplicity and efficiency of this method.

The spatial and time dependent solutions of the Schrödinger equation incorporating the fractional time derivative of distributed order and extending the spatial operator to noninteger dimensions are investigated. They are obtained by using the Green function approach in two situations: the free case and in the presence of a harmonic potential. The results obtained show an anomalous spreading of...