Tbilisi Mathematical Journal

Special functions, integral transforms with applications

Arman Aghili

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Abstract

In this study, the author used integral transforms and a method of the exponential nature to deal with the families of fractional differential equations, Stieltjes type singular integral equations and boundary value problems. Certain integrals involving special functions are evaluated. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.

Note

The author expresses his sincer thanks to the reviewer for the valuable comments and suggestions that lead to a vast improvement in the paper.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 1 (2019), 33-44.

Dates
Received: 1 August 2018
Accepted: 30 November 2018
First available in Project Euclid: 26 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1553565624

Digital Object Identifier
doi:10.32513/tbilisi/1553565624

Mathematical Reviews number (MathSciNet)
MR3954217

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 44A10: Laplace transform 44A15: Special transforms (Legendre, Hilbert, etc.) 44A35: Convolution

Keywords
Laplace transform Stieltjes transform Airy function Riemann-Liouville fractional derivative modified Bessel's functions parabolic cylinder functions

Citation

Aghili, Arman. Special functions, integral transforms with applications. Tbilisi Math. J. 12 (2019), no. 1, 33--44. doi:10.32513/tbilisi/1553565624. https://projecteuclid.org/euclid.tbilisi/1553565624


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