On Some Special Functions for Conformable Fractional Integrals

Year 2020, Volume: 8 Issue: 2, 376 - 383, 27.10.2020

Mehmet Zeki Sarıkaya , Abdullah Akkurt , Hüseyin Budak , Merve Esra Türkay , Hüseyin Yildirim

Abstract

In this paper, we introduce the $\left( \alpha ,k\right) $-gamma function$,\ \left( \alpha ,k\right) $-beta function, Pochhammer symbol $\left( x\right) _{n,k}^{\alpha }\ $and Laplace transforms for conformable fractional integrals. We prove several properties generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. The results presented here would provide generalizations of those given in earlier works.                                                                                                                                                                                                                                                      

Keywords

Gamma function, beta function, Pochhammer symbol, confromable fractional integrals

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