Analytical Solution of Linear Second-Order Non-Homogeneous ‎Fuzzy Partial Differential Equations Using The Fuzzy Sumudu ‎Transform Under Generalized Hukuhara Differentiability

  • Authors

    • Mary Basumatary Department of Mathematics, Central Institute of Technology Kokrajhar, Assam 783370, India
    • Sahalad Borgoyary Department of Mathematics, Central Institute of Technology Kokrajhar, Assam 783370, India
    https://doi.org/10.14419/g9arya79

    Received date: June 16, 2025

    Accepted date: August 21, 2025

    Published date: September 2, 2025

  • Strongly Generalized Hukuhara Differentiability; Fuzzy Sumudu Transform; Initial and Boundary Conditions; Non-Linear Differential ‎Equation; Non-Homogeneous Fuzzy Partial Differential Equation.‎

  • Abstract

    In this paper, a linear second-order non-homogeneous fuzzy partial differential equation (FPDE) is constructed, and the Fuzzy Sumudu ‎Transform (FST) method is applied to solve FPDEs within the context of generalized Hukuhara(gH) differentiability technique. The use ‎of FST, a potent integral transform renowned for its scale-invariant and unit-preserving characteristics, to the fuzzy setting is expanded. ‎FPDEs are solved analytically by transforming them into more straightforward algebraic differential equations in the transform domain, ‎utilizing recent advances in the gH-differentiability technique. Initially, the basic characteristics of linear second-order non-homogeneous FPDEs are presented. To highlight the capabilities, a numerical example is provided.

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    Basumatary, M., & Borgoyary, S. (2025). Analytical Solution of Linear Second-Order Non-Homogeneous ‎Fuzzy Partial Differential Equations Using The Fuzzy Sumudu ‎Transform Under Generalized Hukuhara Differentiability. International Journal of Basic and Applied Sciences, 14(5), 58-75. https://doi.org/10.14419/g9arya79