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

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.

Algebraic Properties of ω , θ -Complex Fuzzy Subgroups

“…Take x � (12) (34), y � (13), and xy � (1432). erefore, (δ (0.7,2π) ∪ c (0.7,2π) ) (x) � 0.7e 2π , (δ (0.7,2π) ∪ c (0.7,2π) ) (y) � 0.6e π/3 and (δ (0.7,2π) ∪ c (0.7,2π) )(xy) � 0.5e π/5 (δ (0.7,2π) ∪ c (0.7, 2π))(xy)≱ min (δ (0.7,2π) ∪ c (0.7,2π) ) 􏽮 (x), (δ (0.7,2π) ∪ c (0.7,2π) )(y)}.…”

“…Imtiaz [28] et al explored the new structure of ξ-complex fuzzy sets and ξ-complex fuzzy subgroups. Many authors [29][30][31][32][33][34] proposed several interesting techniques and approaches to solve complicated systems in fuzzy group theory, fuzzy ring theory, and fuzzy fractional calculus whereas the computational effects are very vague and straightforward. Gulzar [35] et al presented the novel concept of complex fuzzy subfields.…”

New Solutions of Fuzzy-Fractional Fisher Models via Optimal He–Laplace Algorithm

“…Fuzzy noninteger order proportional-integral-derivative (PID) controller scheme is demonstrated for a pneumatic pressure regulating system in [33]. In [34], Arishi has implemented the Shehu transform with a decomposition method to analyze the dispersive KDV equation in the fuzzy environment. Te analytical and numerical solutions of fuzzy-fractional diferential equations were successfully solved in [35] using the fuzzy Laplace transform.…”