Numerical Analysis of the Fractional-Order Telegraph Equations

Azhar, Omar Fouad; Naeem, Muhammad; Mofarreh, Fatemah; Kafle, Jeevan

doi:10.1155/2021/2295804

Cited by 2 publications

(5 citation statements)

References 12 publications

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“…which converges to the exact solution of the classical Hyperbolic Telegraph Equations ( 55) and (56), ω(x, y, t) = e x+y−3t . Further, the obtained solution (66) is fully compatible with the solution investigated via the NDM [20].…”

Section: Numerical Experimentssupporting

confidence: 55%

“…For an integer case of 𝛼 = 1, the exact solution of ( 46) and ( 47) is Example 2. Consider the following nonlinear time-FHTE [20,21]:…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Next, Table 3 presents some numerical comparisons of the outcomes obtained via the proposed method and NDM [20] when α = 1. The provided simulation in Table 3 confirms the superiority and efficiency of our technique, where the numerical results obtained via the Laplace FPSM approach and exact values being faster than the previously mentioned technique.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The two-dimensional time-FHTE is given by [20,21] ∂ 2α t ω(x, y, t) + γω 2 (x, y, t) + µ∂ α t ω(x, y, t) = D 2…”

Section: Introductionmentioning

confidence: 99%

“…Profile solutions for the 𝑗th-MFS-ASs for IVPs (46) and (47) at various values of 𝛼: (a) for 𝑗 = 6; (b) for 𝑗 = 10, for all 𝑡 ∈ [0,1].Example 3. Consider the following linear time-FHTE[20]…”

mentioning

confidence: 99%

See 4 more Smart Citations

A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation

et al. 2023

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In the current analysis, a specific efficient and applicable novel solution approach, based on a fractional power series technique and Laplace transform operator, is considered to predict certain accurate approximate solutions (ASs) for a time-fractional hyperbolic telegraph equation by aid of time-fractional derivatives in a Caputo sense. The solutions are obtained in a fractional Maclurian series formula by solving the original problem in the Laplace space aided by a limit concept having fewer small iterations than the classical fractional power series technique. To confirm applicability and feasibility of the proposed approach, three appropriate initial value problems are considered. Consequently, some simulations of gained outcomes are numerically and graphically implemented to support the effect of the fractional-order parameter on the geometric behavior of the obtained solutions. In addition, graphical representations are also fulfilled to verify the convergence analysis of the fractional series solutions of the classical solution. The proposed technique is therefore proposed to be a straightforward, accurate and powerful approach for handling varied time-fractional models in various physical phenomena.

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Section: Numerical Experimentssupporting

confidence: 55%

“…For an integer case of 𝛼 = 1, the exact solution of ( 46) and ( 47) is Example 2. Consider the following nonlinear time-FHTE [20,21]:…”

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

“…The two-dimensional time-FHTE is given by [20,21] ∂ 2α t ω(x, y, t) + γω 2 (x, y, t) + µ∂ α t ω(x, y, t) = D 2…”

Section: Introductionmentioning

confidence: 99%

mentioning