A Novel Approach to Solving the Fractional Bogoyavlensky Equation via Modified Extended Direct Algebraic Method

Bilal M

Published on: 2024-12-30

Abstract

An advanced modified extended direct algebraic method for solving nonlinear fractional differential equations (FDEs) precisely is presented in this ground-breaking paper. Through the use of a sophisticated fractional complex transformation, we translate nonlinear FDEs with Jumarie modified Riemann-Liouville derivatives into their corresponding ordinary differential equations. Applying the approach to two nonlinear FDEs, including the time-fractional Bogoyavlensky problem, we show its remarkable strength and adaptability. We indisputably demonstrate the effectiveness of the method in solving a wide range of nonlinear FDEs, opening up new avenues for progress in this ever-evolving subject. The significance of this research lies in its capacity to tackle difficult problems in a range of domains, such as physics, engineering, and finance. Our method to nonlinear FDEs is reliable and efficient, which opens up new possibilities for modelling and analysing real-world processes. The subject of fractional calculus, which has garnered a lot of attention recently due to its enhanced ability to characterise complex systems and processes, is also advanced by this study.