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- Title
Study of nonlinear time-fractional hyperbolic-like equations with variable coefficients via semi-analytical technique: Differential -transform method.
- Authors
Singh, Brajesh Kumar; Kumar, A.; Rai, S. N.; Prakasha, D. G.
- Abstract
This work proposes a semi-analytical new hybrid approach, so-called differential -transform method (D TM), to evaluate the behavior of n-space dimensional fractional-nonlinear hyperbolic-like wave equations, where time-fractional derivative is considered in Caputo format. The D TM is the hybrid method in which projected differential transform is implemented after imposing the recently introduced integral transform, i.e., so-called transform [W. Zhao and S. Maitama, J. Appl. Anal. Comput. 10, 1223 (2020)]. The efficiency and applicability of the proposed D TM had been tested by considering three different test examples of the Caputo time-fractional nonlinear hyperbolic-like wave equations in terms of absolute error norms, and the different order D TM solutions are compared with exact solution behaviors and the existing results, for the large time level τ ∈ [ 0 , 1 0 ]. In addition, the convergence analysis of D TM is studied theoretically and verified it numerically as well as graphically, which confirms that the numerical experiments via D TM for distinct fractional orders support the theoretical findings excellently, and the presented D TM results converge to their exact solution behavior, very fast. The evaluated series approximations are expressed in the compact form of Mittag-Leffler functions.
- Subjects
NONLINEAR wave equations; INTEGRAL transforms; WAVE equation; EQUATIONS
- Publication
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2024, Vol 38, Issue 1, p1
- ISSN
0217-9792
- Publication type
Article
- DOI
10.1142/S0217979224500012