Exploring plasma dynamics: Analytical and numerical insights into generalized nonlinear time fractional Harry Dym equation

This investigation aims to examine the resolution of the generalized nonlinear time fractional Harry Dym ðGNTFHDÞ equation through a combined application of analytical and numerical methodologies. The primary objective is to scrutinize the equation's behavior and present pro¯cient methodologies for its resolution. The Khater II analytical technique and numerical frameworks, speci¯cally the Cubic-B-spline, Quantic-B-spline, and Septic-B-spline schemes, are proposed for this purpose. The outcomes of this inquiry yield substantial revelations regarding the characteristics of GNTFHD equation. Both the analytical approach and numerical schemes demonstrate their e±cacy in yielding precise solutions. These ¯ndings carry noteworthy implications across various disciplines, encompassing physics, mathematics, and engineering. The investigated model appears in plasma physics research on soliton theory and nonlinear waves. Soliton waves, which keep their shape and velocity while propagating, are found in plasma physics and other domains. In plasma environments, the Harry Dym equation describes these solitons and their behavior. Solitons are essential for understanding plasma dynamics, including nonlinear waves and structures. They help comprehend plasma dynamics, wave interactions, and other nonlinear processes. The principal deductions drawn from this study underscore the e®ectiveness and viability of the proposed techniques in resolving the GNTFHD equation. This research introduces innovative contributions in terms of insights and methodologies pertinent to analogous nonlinear fractional equations. Its scope encompasses nonlinear dynamics, fractional calculus, and numerical analysis.