Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method

Abstract

The current article discusses the new fuzzy iterative transform method, a hybrid methodology based on fuzzy logic and an iterative transformation technique. We demonstrate the consistency of our technique by employing the Caputo derivative under generalized Hukuhara differentiability to construct fractional fuzzy Klein-Gordon equations with the initial fuzzy condition. The series produced result was calculated and compared to the exact result’s recommended equations. Two problems were used to verify our method, with the results approximated in fuzzy form. The upper and lower half of the fuzzy results were approximated in each of the two examples using two distinct fractional orders between zero and one. Because it globalizes the dynamical behavior of the specified equation, it produces all forms of fuzzy results at any fractional order between 0 and 1. Since fuzzy numbers offer their results in a fuzzy form with lower and upper branches, the unknown amount also adds fuzziness. It is crucial to emphasize that the suggested fuzziness method is intended to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations found in complex and physical structures.