Document Type : Research Paper
Authors
1
Department of Mathematical Sciences, P D Patel Institute of Applied Sciences, Charotar University of Science & Technology, Changa, Gujarat-388421, India.
2
Department of Mathematics, Sardar Vallabhai National Institute of Technology, Surat, India.
Abstract
This manuscript investigates generalized time-fractional Fisher’s equation with fuzzy initial conditions, formulated in the Caputo sense. This problem holds significant importance, as many real-world systems—particularly in biology, ecology, and epidemiology are inherently influenced by memory-dependent dynamics and uncertainties in initial data arising from imprecise measurements or incomplete information. To realistically model this uncertainty, initial conditions are represented using triangular fuzzy numbers, offering a flexible and intuitive approach.} The Reduced Differential Transform Method (RDTM) is employed to address the challenges posed by fractional derivatives and fuzzy initial conditions, owing to its computational efficiency, effectiveness in handling nonlinearities, and capability to generate approximate solutions in the form of a convergent series. Two illustrative examples are presented to validate the proposed approach, with results compared against exact solutions and established numerical methods. These comparisons demonstrate the accuracy, efficacy, and robustness of RDTM in capturing the dynamics of the fuzzy time-fractional Fisher’s equation. Furthermore, graphical analyzes, including surface plots for various fractional orders, illustrate how the solution evolves over time and space, and how different fuzzy initial conditions influence the behavior of the system. Overall, the findings highlight the importance of integrating fractional calculus and fuzzy logic in modeling complex systems under uncertainty.of RDTM in capturing the dynamics of the fuzzy time-fractional Fisher’s equation. Furthermore, graphical analyzes, including surface plots for various fractional orders, illustrate how the solution evolves over time and space, and how different fuzzy initial conditions influence the behavior of the system. Overall, the findings highlight the importance of integrating fractional calculus and fuzzy logic in modeling complex systems under uncertainty.
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