Abstract
The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.
Highlights
Fuzzy set theory is an effective methodology for analyzing unpredictable scenarios
The fuzzy set theory has been widely applied in many domains, i.e., topology, fixed-point theory, integral inequalities, fractional calculus, bifurcation, image processing, consumer electronics, control theory, artificial intelligence, and operations research
This investigation is aimed at providing a semianalytical result to the fuzzy fractional third-order KdV equations by considering the Atangana-Baleanu fractional derivatives
Summary
Fuzzy set theory is an effective methodology for analyzing unpredictable scenarios. Fuzzy fractional calculus theory is a prominent topic of mathematics that spans a wide range of mathematical structures in both theoretical and practical applications In this arena, traditional derivatives are highly reliant on CaputoLiouville or Riemann-Liouville issues. The real-world core replicating dynamic fractional systems, which cannot be denied, must yield a more productive and straightforward definition This orientation introduces a new fractional fuzzy derivative construct, Atangana-Baleanu Caputo, which is used to generate and communicate new concrete fuzzy mathematical ideas. Because the kernel is based on the nature of exponential decay, the new fuzzy fractional Atangana-Baleanu Caputo derivative appears to be releasing singularity with the local kernel function, making fuzzy fractional differential equations more genuine in the creation of diverse uncertain models [21,22,23,24,25].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
