Fractional order calculus: historical apologia, basic concepts and some applications

Some Applications of Fractional Calculus in Engineering

Fractional Calculus FC goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a prelimina...

Introduction to the Concepts and Applications of Fractional and Variable Order Differential Calculus

Understanding the concepts of fractional and variable order differential calculus requires a willingness to depart from the traditional physical interpretations through which calculus is generally understood. Fractional calculus involves the computation of a derivative or integral of any real order, rather than just an integer. Several definitions for calculating a real order derivative or inte...

Historical development and basic concepts

Kronecker operational matrices for fractional calculus and some applications

The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operational matrices for integration and differentiation are studied. we introduce the Kronecker convol...

Fractional calculus and its applications.

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...