A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions

The purpose of this note is to present the different fractional order derivatives definition that are commonly used in the literature on one hand and to present a table of fractional order derivatives of some functions in Riemann-Liouville sense On other the hand. We present some advantages and disadvantages of these fractional derivatives. And finally we propose alternative fractional derivative definition

Majorization for a Class of Analytic Functions Defined by q

We introduce a new class of multivalent analytic functions defined by using q-differentiation and fractional q-calculus operators. Further, we investigate majorization properties for functions belonging to this class. Also, we point out some new and known consequences of our main result

A Generalized q

The aim of this paper is to establish q-extension of the Grüss type integral inequality related to the integrable functions whose bounds are four integrable functions, involving Riemann-Liouville fractional q-integral operators. The results given earlier by Zhu et al. (2012) and Tariboon et al. (2014) follow the special cases of our findings

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions