Authors: Rajković, Predrag M.
Stanković, Miomir S.
Marinković, Sladjana D.
Title: The Laplace transform induced by the deformed exponential function of two variables
Journal: Fractional Calculus and Applied Analysis
Volume: 21
Issue: 3
First page: 775
Last page: 785
Issue Date: 26-Jun-2018
ISSN: 13110454
DOI: 10.1515/fca-2018-0040
URL: https://api.elsevier.com/content/abstract/scopus_id/85050333852
Abstract: 
© 2018 Diogenes Co., Sofia 2018. Based on the easy computation of the direct transform and its inversion, the Laplace transform was used as an effective method for solving differential and integral equations. Its various generalizations appeared in order to be used for treating some new problems. They were based on the generalizations and deformations of the kernel function and of the notion of integral. Here, we expose our generalization of the Laplace transform based on the so-called deformed exponential function of two variables. We point out on some of its properties which hold on in the same or similar manner as in the case of the classical Laplace transform. Relations to a generalized Mittag-Leffler function and to a kind of fractional Riemann-Liouville type integral and derivative are exhibited.
Keywords: convolution | differential operator | exponential function | fractional calculus | integral transform

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