Analysis of Fractional-Order System of One-Dimensional Keller–Segel Equations: A Modified Analytical Method

Abstract

In this paper, an analytical method is implemented to solve fractional-order Keller–Segel equations. The Yang transformation along with the Adomian decomposition method is implemented to obtain the solution of the given problems. The present method has an edge over other techniques as it does not need extra calculations and materials. The validity of the suggested technique is verified by considering some numerical problems. The results obtained confirm the better accuracy of the current technique. The suggested technique has a lesser number of calculations and is straightforward to apply and therefore can be applied to other fractional-order partial differential equations.

Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method

“…Noor and Mohyud-Din [11] used HPM to investigate the solutions of various classical orders of PDEs. For approximate solutions to other classically ordered partial diferential equations by using other methods, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Various methods have been used to investigate the solution to the given nonlinear coupled system (1) of partial diferential equations.…”

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

“…According to Aminikhah and Biazar [18], the Homotopy Perturbation Method (HPM) is a powerful method for solving coupled models of Brusselator and Burger equations that obey a particular set of assumptions. For classically ordered partial differential equations [19][20][21][22][23][24][25][26][27], there are other methods for approximating the solutions. In the last few years, partial differential equations of fractional order have achieved significant advances [28][29][30][31][32][33], because they have been applied to various areas of applied science, including control theory, pattern reorganization, signal processing, identification of systems, and image analysis.…”

A Comparative Study of the Fractional-Order Nonlinear System of Physical Models via Analytical Methods

“…is is why, with the discovery of fractional calculus, it was discovered that FDEs have more real-world applications than ODEs [8,9]. In many mathematical and scienti c elds, FDEs in fractional calculus are one of the most popular subjects, such as biophysics, blood ow phenomena, aerodynamics, viscoelasticity, electrical circuits, electro-analytical chemistry, biology, control theory, nance, hydrology, and control systems [10][11][12][13][14][15].…”