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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3314

Abstract

Laguerre differential equation is a well known equation that appears in the quantum mechanical description of the hydrogen atom. In this paper, we aim to develop a new form of Laguerre Fractional Differential Equation (LFDE) of order $2\alpha$ and we investigate the solutions and their properties. For a positive real number $\alpha$, we prove that the equation has solutions of the form $L_{n,\alpha}(x)=\sum_{k=0}^na_kx^k$, where the coefficients of the polynomials are computed explicitly. For integer case $\alpha=1$ we show that these polynomials are identical to classical Laguerre polynomials. Finally, we solve some fractional differential equations by defining a suitable integral transform.

Keywords

Fractional Laguerre equation, Fractional Sturm-Liouville operator, Riemann-Liouville and Caputo derivatives

First Page

2998

Last Page

3010

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