Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

Abstract

This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

“…In the literature, a number of methods have been developed for the numerical or analytical solutions for FPDEs. We can list some of these methods as follows: Adomian decomposition method [2], the collocation method [3], the fractional differential transform method [4], homotopy analysis method [5], homotopy perturbation method [6], and some other methods [7,8] listed on the references of these papers. In this paper, we present a new method for the analytical solutions of FPDEs.…”

Maximum Norm Error Estimates of ADI Methods for a Two-Dimensional Fractional Subdiffusion Equation

“…Fractional differential equations and fractional calculus arise in various application problems in science and engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Various numerical methods have been developed for the computation of fractional differential equations [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”