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

نویسندگان
Khani, Ali ID 1
Azizi, Mohammad Reza ID 2
Saadatmandi, Abbas ID 3

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

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

3 ‎Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎‎University of Kashan, ‎Kashan‎, ‎Iran

doi
10.22052/mir.2018.96632.1074
چکیده

‎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.

کلیدواژه‌ها
Sinc functions‎, Fractional derivatives‎, ‎Collocation method‎, ‎caputo derivative‎