Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials

Document Type: Original Scientific Paper

Authors

1 ‎Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎‎University of Kashan, ‎Kashan‎, ‎I‎. ‎R‎. ‎Iran

2 Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran

10.22052/mir.2018.96632.1074

Abstract

‎This paper provides the fractional derivatives of‎ ‎the Caputo type for the sinc functions‎. ‎It allows to use efficient‎ ‎numerical method for solving fractional differential equations‎. ‎At‎ ‎first‎, ‎some properties of the sinc functions and Legendre‎ ‎polynomials required for our subsequent development are given‎. ‎Then‎ ‎we use the Legendre polynomials to approximate the fractional‎ ‎derivatives of sinc functions‎. ‎Some numerical examples are‎ ‎introduced to demonstrate the reliability and effectiveness of the‎ ‎introduced method‎.

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