An Advanced Numerical Technique for Solving Nonlinear Fractional-Order Pseudo Hyperbolic Telegraph Equations
Keywords:
stability, approximate results, explicit finite difference technique, Caputo fractional derivative, Nonlinear pseudo hyperbolic telegraph equationsAbstract
In this work, a novel theoretical framework and numerical method for solving nonlinear fractional-order pseudo hyperbolic telegraph equations (FPHTE) are presented. These formulas model the propagation of waves with memory effects in a variety of engineering and physical systems, including electromagnetic waves in plasmas, porous media, and viscoelastic materials. This equation is generated in a generalized form that is not dependent on any particular nonlinearity. This approach shows the correctness and dependability of the method for a variety of these equations by offering a methodical way to identify the mild solution and evaluate its stability. This study investigates how to obtain a numerical approximation of the nonlinear equations using the explicit finite difference approach. The authors develop a finite difference scheme, implement it in MATLAB, and employ various numerical experiments to assess its stability and accuracy. The results demonstrate that the explicit finite difference procedure is a reliable and efficient solution for the proposed framework. It accurately captures wave properties, including memory and nonlinearity effects, and is stable over a wide range of fractional orders. Maintaining numerical stability and accuracy requires careful consideration of the time step, spatial grid size, and fractional order.
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Copyright (c) 2026 Sadeq Taha Abdulazeez, Mahmut Modanlı, Şakir Işleyen, Ali Akgül (Author)
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