Analytical and semi‐analytical solutions for time‐fractional Cahn–Allen equation. (4th November 2020)

• Record Type: Journal Article
• Authors: Khater, Mostafa M. A.; Bekir, Ahmet; Lu, Dianchen; Attia, Raghda A. M.
• Other Names: Kirane Mokhtar guestEditor.; Srivastava Hari M. guestEditor.; Zhou Yong guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 3(2021)
• Page Start: 2682
• Page End: 2691
• Publication Date: 2020-11-04
• Subjects: Adomian decomposition method -- modified auxiliary equation method (modified Khater method) -- time‐fractional Cahn–Allen equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6951
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper investigates the analytical and semi‐analytical solutions of the time‐fractional Cahn–Allen equation, which describes the structure of dynamic for phase separation in Fe‐Cr‐X (X = Mo, Cu) ternary alloys. We apply a modified auxiliary equation method and the Adomian decomposition method to get distinct solutions to our suggested model. These solutions describe the dynamic of the phase separation in iron alloys and use in solidification and nucleation problems. The applications of this method arise in many various fields such as plasma physics, quantum mechanics, mathematical biology, and fluid dynamics. We apply a conformable fractional derivative to this fractional model to convert it into a nonlinear partial differential equation with integer order. We obtain many analytical wave solutions and also apply a semi‐analytical scheme to calculate the absolute value of error. All solutions are verified by using Mathematica software.