### AIMS Mathematics

2022, Issue 5: 9443-9462. doi: 10.3934/math.2022524
Research article Special Issues

# Mellin transform for fractional integrals with general analytic kernel

• Received: 27 November 2021 Revised: 21 January 2022 Accepted: 10 February 2022 Published: 14 March 2022
• MSC : Primary: 58F15, 58F17; Secondary: 53C35

• Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order $\varsigma\ge0$ and $\varrho$ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.

Citation: Maliha Rashid, Amna Kalsoom, Maria Sager, Mustafa Inc, Dumitru Baleanu, Ali S. Alshomrani. Mellin transform for fractional integrals with general analytic kernel[J]. AIMS Mathematics, 2022, 7(5): 9443-9462. doi: 10.3934/math.2022524

### Related Papers:

• Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order $\varsigma\ge0$ and $\varrho$ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.

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