Mikusiński's operational calculus for Prabhakar fractional calculus. Issue 12 (2nd December 2022)

• Record Type: Journal Article
• Authors: Rani, Noosheza; Fernandez, Arran
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 12(2022)
• Page Start: 945
• Page End: 965
• Publication Date: 2022-12-02
• Subjects: Fractional calculus -- operational calculus -- fractional differential equations -- Mikusinski's operational calculus -- Prabhakar fractional calculus; 26A33 -- 44A40 -- 34A08 -- 33E12; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2022.2057970
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: The operational calculus method of Mikusiński is a powerful yet underappreciated theory, enabling differential equations to be solved using abstract algebra. We interpret the fractional integrals and derivatives of Prabhakar type within Mikusiński's theory, by defining them on appropriate function spaces and using judiciously their fundamental properties such as semigroup and series formulae. This theoretical framework enables explicit solutions to be found, for the first time, for a general class of linear Prabhakar fractional differential equations, with the solutions expressed as double or multiple infinite series.