A note on hybrid VIM approach for a type of fractional Lane-Emden equations
Lok Nath Kannaujia, Amit Kumar Verma
Department of Mathematics, Indian Institute of Technology Patna, Bihta, Bihta, India
Keywords: α-analytic, α-singular, Lane-Emden, Jumarie fractional derivative, Caputo fractional derivative
Abstract
In this article, we introduce a class of nonlinear fractional Lane-Emden equations incorporating Jumarie's fractional derivative with Neumann boundary conditions. To compute approximate numerical solutions, we propose an efficient modification of a variational iteration method (VIM) termed the fractional variational iteration method (FrVIM). Notably, for the limiting case our problem reduces to the classical Lane-Emden equation. We illustrate the effectiveness of our approach through graphical representations of solutions obtained using both Jumarie and Caputo derivatives. Furthermore, we observe that when the order of derivative approaches 1, the fractional solution plots gradually converge to the classical solution, demonstrating the accuracy and reliability of our method.
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