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<p>In this paper, the time fractional pseudo-hyperbolic telegraph equation is investigated using the space-time linear Legendre multiwavelet method (STLLM). The behavior of the model is governed by a dominant mixed derivative term. This complex structure contains a fractional-order time derivative as well as a first-order integer derivative that forms a mixed spatial-temporal term, which makes it more challenging. A Riemann-Liouville fractional integral operator for linear Legendre multiwavelet (RFLLM) is derived to handle this hybrid system. Both the space and temporal derivatives are discretized using STLLM and RFLLM, which transforms the problem into a system of algebraic equations. Solving this system yields the unknown wavelet coefficients and subsequently the approximate solution. The convergence analysis of the method is established. Two benchmark problems are solved using the proposed method for computational convergence analysis. The obtained results are compared with existing results in the literature, which demonstrates that the STLLM method is more accurate.</p>

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A novel space-time linear Legendre multiwavelet method for time fractional pseudo-hyperbolic telegraph equation

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Mo Faheem

摘要

In this paper, the time fractional pseudo-hyperbolic telegraph equation is investigated using the space-time linear Legendre multiwavelet method (STLLM). The behavior of the model is governed by a dominant mixed derivative term. This complex structure contains a fractional-order time derivative as well as a first-order integer derivative that forms a mixed spatial-temporal term, which makes it more challenging. A Riemann-Liouville fractional integral operator for linear Legendre multiwavelet (RFLLM) is derived to handle this hybrid system. Both the space and temporal derivatives are discretized using STLLM and RFLLM, which transforms the problem into a system of algebraic equations. Solving this system yields the unknown wavelet coefficients and subsequently the approximate solution. The convergence analysis of the method is established. Two benchmark problems are solved using the proposed method for computational convergence analysis. The obtained results are compared with existing results in the literature, which demonstrates that the STLLM method is more accurate.