On Laplace transforms with respect to functions and their applications to fractional differential equations. (12th September 2021)

• Record Type: Journal Article
• Authors: Fahad, Hafiz Muhammad; Rehman, Mujeeb ur; Fernandez, Arran
• Other Names: Singh Jagdev guestEditor.; Kumar Devendra guestEditor.; Baleanu Dumitru guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 7(2023)
• Page Start: 8304
• Page End: 8323
• Publication Date: 2021-09-12
• Subjects: fractional calculus -- fractional differential equations -- generalised fractional operators -- Laplace transform -- Ψ‐fractional calculus; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7772
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called Ψ‐fractional calculus. The operational calculus approach has proved useful for understanding and extending this topic of study. Motivated by fractional differential equations, we present an operational calculus approach for Laplace transforms with respect to functions and their relationship with fractional operators with respect to functions. This approach makes the generalised Laplace transforms much easier to analyse and to apply in practice. We prove several important properties of these generalised Laplace transforms, including an inversion formula, and apply it to solve some fractional differential equations, using the operational calculus approach for efficient solving.