Numerical Solution of Time-Fractional Emden–Fowler-Type Equations Using the Rational Homotopy Perturbation Method

Abstract

The integral-order derivative is not suitable where infinite variances are expected, and the fractional derivative manages to consider effects with more precision; therefore, we considered time-fractional Emden–Fowler-type equations and solved them using the rational homotopy perturbation method (RHPM). The RHPM method is based on two power series in rational form. The existence and uniqueness of the equation are proved using the Banach fixed-point theorem. Furthermore, we approximate the term h(z) with a polynomial of a suitable degree and then solve the system using the proposed method and obtain an approximate symmetric solution. Two numerical examples are investigated using this proposed approach. The effectiveness of the proposed approach is checked by representing the graphs of exact and approximate solutions. The table of absolute error is also presented to understand the method’s accuracy.

Approximate‐analytical iterative approach to time‐fractional Bloch equation with Mittag–Leffler type kernel

“…Fractional calculus has become a potentially useful tool in a number of scientific and engineering fields, including fluid dynamics [3][4][5], physics [6,7], and biology [8][9][10]. Integer order derivative is local, whereas fractional derivative is nonlocal in nature.…”

New Trends on the Mathematical Models and Solitons Arising in Real-World Problems

“…In [35], the authors considered time-fractional Emden-Fowler-type equations and solved them using the rational homotopy perturbation method (RHPM). The RHPM is based on two power series in rational form.…”