Analytic technique for solving temporal time-fractional gas dynamics equations with Caputo fractional derivative

Constructing mathematical models of fractional order for real-world problems and developing numeric-analytic solutions are extremely significant subjects in diverse fields of physics, applied mathematics and engineering problems. In this work, a novel analytical treatment technique called the Laplace residual power series (LRPS) technique is performed to produce approximate solutions for a non-linear time-fractional gas dynamics equation (FGDE) in a multiple fractional power series (MFPS) formula. The LRPS technique is a coupling of the RPS approach with the Laplace transform operator. The implementation of the proposed technique to handle time-FGDE models is introduced in detail. The MFPS solution for the target model is produced by solving it in the Laplace space by utilizing the limit concept with fewer computations and more accuracy. The applicability and performance of the technique have been validated via testing three attractive initial value problems for non-linear FGDEs. The impact of the fractional order beta on the behavior of the MFPS approximate solutions is numerically and graphically described. The jth MFPS approximate solutions were found to be in full harmony with the exact solutions. The solutions obtained by the LRPS technique indicate and emphasize that the technique is easy to perform with computational efficiency for different kinds of time-fractional models in physical phenomena.

Automated summary

Constructing mathematical models of fractional order and developing numeric-analytic solutions are significant subjects in physics, applied mathematics, and engineering. This study introduces a novel analytical technique called the Laplace residual power series (LRPS) technique to produce approximate solutions for a non-linear time-fractional gas dynamics equation. The technique combines the RPS approach with the Laplace transform operator and has been successfully applied to handle time-FGDE models, generating accurate solutions with fewer computations. The impact of the fractional order on the solutions is also investigated.