Solution of Equations with q-Derivatives and Ward’s Derivatives Using an Operational Method

Bengochea, Gabriel; Verde-Star, Luís; Ortigueira, Manuel

http://hdl.handle.net/10362/158000

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Autores

Bengochea, Gabriel

Verde-Star, Luís

Ortigueira, Manuel

Resumo(s)

We show that several types of differential equations that involve q-derivatives, Fibonacci deriva-tives, and other Ward’s derivatives, can be solved by an algebraic operational method that does not use integrals nor integral transforms. We deal with extensions of the Ward’s derivatives that can be applied to formal Laurent series. Several examples of linear and nonlinear equations are presented.

Descrição

Funding Information: 2020 Mathematics Subject Classification. Primary 44A40, 34A06, 39A13 Keywords. Operational calculus; q-calculus; Ward’s calculus Received: 10 May 2021; Accepted: 26 October 2021 Communicated by Hari M. Srivastava Corresponding author: Gabriel Bengochea. Email addresses: gabriel.bengochea@uacm.edu.mx (Gabriel Bengochea), verde@xanum.uam.mx (Luis Verde-Star), mdo@fct.unl.pt (Manuel Ortigueira) Publisher Copyright: © 2022, University of Nis. All rights reserved.