An Analytical Algebraic Method for Solving Nonlinear Fractional Differential Equations with Conformable Fractional Derivatives (Contemporary Mathematics, 2025)
This paper presents a new and enhanced algebraic method for accurately solving nonlinear Fractional Differential Equations (FDEs). Using a complex fractional transformation, we translate nonlinear FDEs with Jumarie modified Riemann-Liouville derivatives into their corresponding ordinary differential equations. By applying this method to two nonlinear FDEs, including the time-fractional Bogoyavlenskii problem, we demonstrate its strength and adaptability. The method’s effectiveness in solving various nonlinear FDEs is showcased, laying the groundwork for future developments in this rapidly evolving field. This research has significant implications for addressing complex issues in physics, engineering, and finance, providing a reliable and efficient approach to modeling and analyzing realworld systems. Furthermore, this study advances the field of fractional calculus, which has garnered attention for its ability to illustrate and explain intricate systems and processes.
Keywords: nonlinear fractional differential equation, algebraic method, fractional complex transformation, conformable fractional derivative, time-fractional bogoyavlenskii problem