Comparison of Caputo and Atangana–Baleanu fractional derivatives for the pseudohyperbolic telegraph differential equations

Modanlı, Mahmut

doi:10.1007/s12043-021-02250-6

Cited by 7 publications

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The numerical solutions for the suggested model (1) were derived by [31] using the Dufort Frankel difference scheme approach. Since the Caputo derivative [30] is the most frequently utilized derivative characteristic in the literature on fractional analysis, we adopted it in our model.…”

Section: Introductionmentioning

confidence: 99%

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Abdulazeez

Modanlı

2023

International Journal of Mathematics and Computer in Engineering

Self Cite

View full text Add to dashboard Cite

The Pseudo-Hyperbolic Telegraph partial differential equation (PHTPDE) based on the Caputo fractional derivative is investigated in this paper. The modified double Laplace transform method (MDLTM) is constructed for the proposed model. The MDLTM was used to obtain the analytic solution for the pseudo-hyperbolic telegraph equation of fractional order defined by the Caputo derivative. The proposed method is a highly effective analytical method for the fractional-order pseudo-hyperbolic telegraph equation. A test problem was presented as an example. Based on the results, it is clear that this method is more convenient and produces an analytic solution in fewer steps than other methods that require more steps to have an identical analytical solution. This paper claims to provide an analytic solution to the fractional order pseudohyperbolic telegraph equation using the MDLTM. An analytical solution directs to an exact, closed-form solution that can be expressed in mathematical functions or known operations. Obtaining analytic solutions to PDEs is often challenging, especially for fractional order equations, making this achievement noteworthy.

show abstract

Section: Introductionmentioning

confidence: 99%