Korean J. Math.  Vol 27, No 2 (2019)  pp.487-503
DOI: https://doi.org/10.11568/kjm.2019.27.2.487

Certain results involving fractional operators and special functions

Arman Aghili

Abstract


In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper. 


Keywords


Laplace transforms; Fourier transforms; Kr\"atzel function; Hankel transforms; Riemann - Liouville fractional derivative.

Subject classification

26A33; 44A10; 44A15; 44A35

Sponsor(s)

University of Guilan

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