This paper presents the application of Fractional Order PID controller as a supplementary controller to improve the dynamics of LFC in multi area deregulated power system. FOPID is a PID controller whose derivative and integral orders are of fractional rather than integer. The extension of derivative and integration order from integer to fractional order provides more flexibility in design of t...

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and ...

This study demonstrates the total control of a class hybrid neutral fractional evolution equations with non-instantaneous impulses and non-local conditions. The boundary value problem conditions is created using Caputo derivative order 1<α≤2. In to create novel, strongly continuous associated operators, infinitesimal generator sine cosine families examined. Additionally, two approaches are u...

Fractional centred differences and derivatives definitions are proposed generalising to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalisations of the Cauchy integral derivative. To compute this integral, a special two straight line path was use...

In this paper, we present a finite difference scheme for a class of time fractional diffusion equation with variable coefficient, where the fractional derivative is defined by the Caputo derivative. The present algorithm is unconditionally stable, and possess spatial sixth order and temporal 2 − α order accuracy, which is an improvement of the spatial fourth order accuracy in the existing resul...

Local fractional calculus (fractal calculus) plays a crucial role in applications, especially computer sciences and engineering. One of these applications appears the theory chaos. Therefore, this paper studies dynamics fractal complex logistic map then employs to generate chaotic sequences for new symmetric image encryption algorithm. Firstly, we derive investigate its by determining equilibri...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

In this paper we present an extension of Fractional Laplace Transform in the framework non-conformable local fractional derivative. Its main properties are studied and it is applied to resolution differential equations.

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...