Laplace transform collocation method for telegraph equations defined by Caputo derivative

Mahmut Modanlı; Mehmet Emir Koksal

doi:10.53391/mmnsa.2022.014

Authors

Mahmut Modanlı Department of Mathematics, Harran University, 63300 Sanliurfa, Türkiye https://orcid.org/0000-0002-7743-3512
Mehmet Emir Koksal Department of Mathematics, Ondokuz Mayis University, 55139 Samsun, Türkiye; Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands https://orcid.org/0000-0001-7049-3398

DOI:

https://doi.org/10.53391/mmnsa.2022.014

Keywords:

Caputo fractional derivative, collocation method, telegraph equation, approximation solution, error analysis

Abstract

The purpose of this paper is to find approximate solutions to the fractional telegraph differential equation (FTDE) using Laplace transform collocation method (LTCM). The equation is defined by Caputo fractional derivative. A new form of the trial function from the original equation is presented and unknown coefficients in the trial function are computed by using LTCM. Two different initial-boundary value problems are considered as the test problems and approximate solutions are compared with analytical solutions. Numerical results are presented by graphs and tables. From the obtained results, we observe that the method is accurate, effective, and useful.

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