Analysing soliton dynamics and a comparative study of fractional derivatives in the nonlinear fractional Kudryashov's equation

In this scholarly exploration, we employ new mapping method to unveil new soliton solutions to the nonlinear fractional Kudryashov's equation, using β-derivative and M-Truncated fractional derivatives. Soliton phenomena, invaluable for enhancing computational capabilities in computer systems, find particular utility in tasks like data analysis, image processing, and simulations across various computer science domains. Our research reveals diverse solution forms, encompassing dark, periodic, kink, singular, dark-bright, and bright solitons. These versatile soliton types offer adaptable tools for both modelling and simulation. To enhance understanding, we provide 3D and 2D graphical representations, which facilitate a comparative analysis of solutions derived from the two fractional derivatives. Additionally we compare the effects of different fractional derivative operators (β-derivative and M-Truncated derivative) involve in the nonlinear fractional Kudryashov's equation. The incorporation of both derivatives allows for a broader exploration of solution forms and enhance the understanding of the equation's behaviour and its solution. Our work bridges soliton physics and computer science, underscoring the significance of soliton phenomena in advancing computational modelling and simulations. This research contributes to the intersection of theoretical mathematics and practical computer science, highlighting the vital role of solitons in scientific fields.