leroy型多指标mittagleffler - prabhakar函数的拉普拉斯变换(第1部分)

Q3 Mathematics International Journal of Applied Mathematics Pub Date : 2023-10-16 DOI:10.12732/ijam.v36i4.2

J. Paneva-Konovska, V. Kiryakova, S. Rogosin, M. Dubatovskaya

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LAPLACE TRANSFORM (PART 1) OF THE MULTI-INDEX MITTAG-LEFFLER-PRABHAKAR FUNCTIONS OF LE ROY TYPE

: In this paper, the multi-index generalizations (with 3 and 4 indices, then with 3 m and 4 m indices) of the classical Le Roy function and its Mittag-Leﬄer analogues are considered on wider sets of the parameters. Thus, we extend our recent studies as continuation of the works on Le Roy type functions by Gerhold, Garra and Polito, Mainardi and Garrappa, Tomovski and Mehrez, Pogany, Gorska and Horzela, etc. The Laplace transforms of these multi-index Le Roy type functions are provided. In next Part 2, we will propose their images under the Erd´elyi-Kober operators of fractional calculus. The results are speciﬁed for the particular cases of the considered functions. Finally, we discuss some open problems about relation of the Le Roy type functions with special functions more general than the Fox H -functions.

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来源期刊

International Journal of Applied Mathematics Mathematics-Mathematics (all)

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： The journal is peer-reviewed and publishes carefully selected original research papers on all scopes of mathematics and its applications: combinatorics, design and configurations, graph theory, fractals, lattices, ordered algebraic structures, real functions, measure and integration, functions of complex variable, potential theory, special functions, fractional calculus, operational calculus and integral transforms, dynamical systems in their broadest sense (covering ODEs, all kinds of PDEs, FDEs, difference equations, functional equations), approximation and expansion, integral equations, operator theory, calculus of variations, optimal control, optimization, applied differential geometry, probability theory and stochastic processes, statistics, numerical analysis, computer science, mechanics of particle and systems, mechanics of solids, fluid mechanics, classical thermodynamics, mathematical methods in economics, operations research, programming, mathematical biology, systems theory, information and communication, circuits.