EconPapers    
Economics at your fingertips  
 

Time-fractional telegraph equation with ψ-Hilfer derivatives

N. Vieira, M. Ferreira and M.M. Rodrigues

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

Abstract: This paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with ψ-Hilfer fractional derivatives. By application of the Fourier and ψ-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables in the space-time domain. A double series representation of the first fundamental solution is deduced for the case of odd dimension. The results derived here are of general nature since our fractional derivatives allow to interpolate between Riemann-Liouville and Caputo fractional derivatives and the use of an arbitrary positive monotone increasing function ψ in the kernel allows to encompass most of the fractional derivatives in the literature. In the one dimensional case, we prove the conditions under which the first fundamental solution of our equation can be interpreted as a spatial probability density function evolving in time, generalizing the results of Orsingher and Beghin (2004). Some plots of the fundamental solutions for different fractional derivatives are presented and analysed, and particular cases are addressed to show the consistency of our results.

Keywords: Time-fractional telegraph equation; ψ-Hilfer fractional derivative; ψ-Laplace transform; Series and integral representations; Fractional moments; Probability density function (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922004866
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922004866

DOI: 10.1016/j.chaos.2022.112276

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().

 
Page updated 2025-05-25
Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922004866