Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach....

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach....

Recently much of the research has been dedicated to the application of fractional calculus in rheology. In this paper fractional-order spectra are presented for the complex viscoelastic materials, which mechanical analogy are constructed by fractional elements connected in series or parallel. Fractional-order spectra connect directly to the material’s constitutive relation with fractional deriv...

In this work, a new control scheme for synchronization of AC microgrids with upstream power grid is presented. The effects of V2Gs (vehicle to grid) dynamics on synchronization process is studied. This new control approach is based on the optimal fractional calculus and has been developed for synchronization of the microgrid. The V2Gs effect on the dynamics of the microgrid is analyzed through ...

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact, this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and i...

Abstract The realization of fractional quantum chemistry is presented. Adopting the integro‐differential operators calculus arbitrary‐order, we develop a general framework for description nonlocal effects in complex electronic environments. After brief overview historical and fundamental aspects various classes Schrödinger equations are discussed pertinent controversies open problems around the...

The major contribution of this paper is to introduce the fractional calculus used to develop a fractional-order model for the DC electrical drive and, based on it, to design a fractional adaptive controller. In such a context, two modifications of the conventional Model Reference Adaptive Control theory are presented. Based on simulation results obtained in Matlab/ Simulink, the benefits of fra...