Avit, Özkan; Anac, Halil

The present study used the novel conformable fractional methods to examine the nonlinear Kuramoto-Sivashinsky equations of the conformable fractional derivative. The Kuramoto-Sivashinsky equation is a mathematical model employed to elucidate a diverse range of chemical and physical phenomena, encompassing chemical reaction-diffusion processes, plasma instabilities, viscous flow issues, flame front propagation, and magnetized plasmas. The present inquiry provides an examination of convergence and error for the future scheme. The conformable q-homotopy analysis transform method (Cq-HATM) provides h-curves that illustrate the convergence range of the series solution achieved. In order to validate the effectiveness and suitability of the Cq-HATM, we examine separate instances. In this study, we introduce an application that demonstrates the potential benefits and effectiveness of the proposed approach. Furthermore, an error analysis is performed in order to verify the accuracy of the scheme. Numerical simulations are conducted to validate the precision of the forthcoming approach. The findings obtained from the numerical and graphical analyses are presented in this study. The method provided in this study showcases a notable degree of computational precision and ease in examining and resolving intricate phenomena related to conformable fractional nonlinear partial differential equations within the domains of science and technology.

Anac, Halil; Merdan, Mehmet; Kesemen, Tulay

The series solutions of the random nonlinear partial differential equations have been examined by a hybrid method. The random nonlinear partial differential equations are studied by both normal and uniform distributions. Two initial-value problems are indicated to exemplify the influence of the solutions acquired by the hybrid method. Also, the functions for the first and second moments of the approximate solutions of random nonlinear partial differential equations are acquired in the MAPLE software. The hybrid method is implemented to analyze the solutions of the random nonlinear partial differential equations. MAPLE software is used to find the solutions. Besides, MAPLE software is used for the drawing the figures.

Anac, Halil

In this paper, the nonlinear system of local fractional partial differential equations is solved via local fractional Elzaki transform decomposition method. The local fractional Elzaki decomposition transform method combines a local fractional Elzaki transform and the Adomian decomposition method. Applications related to the nonlinear system of local fractional partial differential equations are presented.