In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

Differential and integral calculus belongs to basic courses of mathematics and everybody understands geometrical and physical meaning of derivative or integral. But, hardly anybody can imagine for example derivative of order 1/2 or even of non-rational order. The branch of mathematics which generalizes calculus to non-integer case is known under the term “fractional calculs” although this name ...

In this paper, a high-performance optimal fractional emotional intelligent controller for an Automatic Voltage Regulator (AVR) in power system using Cuckoo optimization algorithm (COA) is proposed. AVR is the main controller within the excitation system that preserves the terminal voltage of a synchronous generator at a specified level. The proposed control strategy is based on brain emotional ...

This paper presents the application of a direct Fractional Order Model Reference Adaptive Controller (FOMRAC) to an Automatic Voltage Regulator (AVR). A direct FOMRAC is a direct Model Reference Adaptive Control (MRAC), whose controller parameters are adjusted using fractional order differential equations. Four realizations of the FOMRAC were designed in this work, each one considering differen...

As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

Electrohydraulic servo system has been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In order to in-crease the reliability, controllability and utilizing the superior speed of response achievable from electrohydraulic systems, further research is required to develop a control soft...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

Proportional Integral Derivative (PID) controller is one of the most classical controllers, which has a good performance in industrial applications. The traditional PID parameter tuning relies on experience, however, intelligent algorithm used to optimize controller, makes it more convenient. Fish Migration Optimization (FMO) an excellent that mimics swim and migration behaviors fish biology. E...

In this paper, tuning of power system stabilizer (PSS) and thyristor controlled series capacitor (TCSC) is studied. The analysis of mode controllability is used to select the effective location for TCSC. The performances of TCSC equipped with a proportional-integral-derivative controller (P-I-D controller) and proportional-integral-derivative power system stabilizer (P-I-D PSS) are investigated...