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The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations

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  • Bouchra Ben Amma
  • Said Melliani
  • Lalla Saadia Chadli

Abstract

In this paper, we consider intuitionistic fuzzy partial functional differential equations with local and nonlocal initial conditions using the Banach fixed point theorem. A new complete intuitionistic fuzzy metric space is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems. We use the level-set representation of intuitionistic fuzzy functions and define the solution to an intuitionistic fuzzy partial functional differential equation problem through a corresponding parametric problem and further develop theoretical results on the existence and uniqueness of the solution. An example is presented to illustrate the results with some numerical simulation for - cuts of the intuitionistic fuzzy solutions: we give the representation of the surface of intuitionistic fuzzy solutions.

Suggested Citation

  • Bouchra Ben Amma & Said Melliani & Lalla Saadia Chadli, 2019. "The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-13, July.
    • Handle: RePEc:hin:jnijde:9210641
    DOI: 10.1155/2019/9210641
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