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<p>In this paper, we propose two alternative approaches to solve the fuzzy time-fractional Newell–Whitehead–Segel problem. In nonlinear systems, the fuzzy Newell–Whitehead–Segel equation effectively explains the appearance of the stripe patterns in two-dimensional systems. The presented approaches are used to solve some case study problems from fuzzy Newell–Whitehead–Segel using the Atangana–Baleanu fractional derivative operator and the Laplace transform. The exact and analytical results are compared with one another using graphs and tables to demonstrate the efficacy of the suggested methods. The results of applying proposed techniques at various fractional orders are compared, which demonstrates that when a value trends from fractional order to integer order, a solution approaches the exact solution. Furthermore, we provide the solution of the fuzzy time-fractional Klein–Fock–Gordon (FFKFG) equation using the fuzzy <i>q</i>-homotopy analysis transform method (<i>q</i>-HATM). Using Banach’s theory of fixed points, the uniqueness and convergence analysis for the proposed problem are demonstrated. The numerical simulation was provided to demonstrate the effectiveness and dependability of the suggested method. Moreover, several fractional orders have been used to capture the behavior of the given solution. The results show that the suggested method is particularly good at analyzing the behavior of complicated problems that arise in science and engineering. The provided approaches to solving diverse nonlinear fuzzy fractional-order partial differential equations are interesting, easy, and very accurate.</p>

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On the Fuzzy Solutions of Nonlinear Fractional Partial Differential Equations

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Mawia Osman,
  • Usman Ali,
  • Sarmad A. Altaie,
  • Ali Fareed Jameel,
  • Omer Abdalrhman Omer,
  • Altyeb Mohammed Mustafa

摘要

In this paper, we propose two alternative approaches to solve the fuzzy time-fractional Newell–Whitehead–Segel problem. In nonlinear systems, the fuzzy Newell–Whitehead–Segel equation effectively explains the appearance of the stripe patterns in two-dimensional systems. The presented approaches are used to solve some case study problems from fuzzy Newell–Whitehead–Segel using the Atangana–Baleanu fractional derivative operator and the Laplace transform. The exact and analytical results are compared with one another using graphs and tables to demonstrate the efficacy of the suggested methods. The results of applying proposed techniques at various fractional orders are compared, which demonstrates that when a value trends from fractional order to integer order, a solution approaches the exact solution. Furthermore, we provide the solution of the fuzzy time-fractional Klein–Fock–Gordon (FFKFG) equation using the fuzzy q-homotopy analysis transform method (q-HATM). Using Banach’s theory of fixed points, the uniqueness and convergence analysis for the proposed problem are demonstrated. The numerical simulation was provided to demonstrate the effectiveness and dependability of the suggested method. Moreover, several fractional orders have been used to capture the behavior of the given solution. The results show that the suggested method is particularly good at analyzing the behavior of complicated problems that arise in science and engineering. The provided approaches to solving diverse nonlinear fuzzy fractional-order partial differential equations are interesting, easy, and very accurate.