<p>Nonlinear time-fractional partial differential equations (NTFPDEs) play a significant role in modeling various complex phenomena in science and engineering. However, obtaining analytical solutions to these equations is often challenging because of their nonlinear and fractional nature. To efficiently solve NTFPDEs, we propose a new hybrid analytical technique called the Hybrid Laplace Adomian Variational Iteration Method (HLAVIM), which is a combination of the Laplace Adomian Decomposition Method (LADM) and the Laplace Variational Iteration Method (LVIM). To verify the effectiveness, validity, and accuracy of the proposed method, four examples of nonlinear time-fractional partial differential equations are solved, and the results are presented both numerically and graphically. These results are compared with those obtained using existing methods as well as with the exact solutions. The comparison demonstrates that the proposed method yields more accurate results than existing methods, and the approximate solution closely matches the exact solution within just a few iterations. Therefore, the proposed method is efficient and effective and can be applied to a wide range of NTFPDEs.</p>

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A new hybrid Laplace Adomian variational iteration method for solving nonlinear time-fractional partial differential equations

  • Monowar Hossain,
  • Mohammed Aman Ullah

摘要

Nonlinear time-fractional partial differential equations (NTFPDEs) play a significant role in modeling various complex phenomena in science and engineering. However, obtaining analytical solutions to these equations is often challenging because of their nonlinear and fractional nature. To efficiently solve NTFPDEs, we propose a new hybrid analytical technique called the Hybrid Laplace Adomian Variational Iteration Method (HLAVIM), which is a combination of the Laplace Adomian Decomposition Method (LADM) and the Laplace Variational Iteration Method (LVIM). To verify the effectiveness, validity, and accuracy of the proposed method, four examples of nonlinear time-fractional partial differential equations are solved, and the results are presented both numerically and graphically. These results are compared with those obtained using existing methods as well as with the exact solutions. The comparison demonstrates that the proposed method yields more accurate results than existing methods, and the approximate solution closely matches the exact solution within just a few iterations. Therefore, the proposed method is efficient and effective and can be applied to a wide range of NTFPDEs.