Novel Evaluation of Fuzzy Fractional Helmholtz Equations

The current article discusses the fuzzy new iterative transform approach, which is a combination of a fuzzy hybrid methodology and an iterative transformation technique. We establish the consistence of our strategy by obtaining fractional fuzzy Helmholtz equations with the initial fuzzy condition using the Caputo derivative under generalized Hukuhara differentiability. The series obtained result was calculated and compared to the proposed equations of the actual result. Three challenges were provided to validate our method, and the outcomes were approximated in fuzzy form. In each of the three examples, the upper and bottom halves of the fuzzy solution were approximated utilizing two various fractional order between 0 and 1. Due to the fact that it globalizes the dynamical behavior of the specified equation, it produces all forms of fuzzy results at any fractional order between 0 and 1. Due to the fact that the fuzzy numbers presents the result in a lower and upper branches fuzzy type, the unknown quantity incorporates fuzziness as well. It is critical to emphasize that the purpose of the proposed fuzziness approach is to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations that arise in complex and physical structures.

Automated summary

The article discusses the fuzzy new iterative transform approach, which combines a fuzzy hybrid methodology and an iterative transformation technique. By obtaining fractional fuzzy Helmholtz equations with initial fuzzy conditions using the Caputo derivative under generalized Hukuhara differentiability, the consistency of the strategy is established. The outcomes are approximated in fuzzy form through three challenges, where the upper and bottom halves of the fuzzy solution are approximated using two different fractional orders between 0 and 1 in each of the three examples.