Study of Fuzzy Fractional Third-Order Dispersive KdV Equation in a Plasma under Atangana-Baleanu Derivative

Author:

Areshi Mounirah1ORCID,El-Tantawy S. A.23ORCID,Alotaibi B. M.4,Zaland Shamsullah5ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

2. Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt

3. Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Saudi Arabia

4. Department of Physics, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

5. Faculty of Mathematics, Kabul Polytechnic University, Afghanistan

Abstract

Motivated by the wide-spread of both integer and fractional third-order dispersive Korteweg-de Vries (KdV) equations in explaining many nonlinear phenomena in a plasma and many other fluid models, thus, in this article, we constructed a system for calculating an analytical solution to a fractional fuzzy third-order dispersive KdV problems. We implemented the Shehu transformation and the iterative transformation technique under the Atangana-Baleanu fractional derivative. The achieved series result was contacted and determined the analytic value of the suggested models. For the confirmation of our system, three various problems have been represented, and the fuzzy type solution was determined. The fuzzy results of upper and lower section of all three problems are simulate applying two different fractional orders among zero and one. Because it globalises the dynamic properties of the specified equation, it delivers all forms of fuzzy solutions occurring at any fractional order among zero and one. The present results can help many researchers to explain the nonlinear phenomena that can create and propagate in several plasma models.

Funder

Princess Nourah Bint Abdulrahman University

Publisher

Hindawi Limited

Subject

Analysis

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