Open AccessANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIEDq-HATM
Author(s) -
Nehad Ali Shah,
Praveen Agarwal,
Jae Dong Chung,
Saad Althobaiti,
S. M. Sayed,
Abdulrahman F. Aljohani,
Mohamed Alkafafy
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x22400126
Subject(s) - homotopy analysis method , mathematics , convergence (economics) , fractional calculus , nonlinear system , sequence (biology) , partial differential equation , operator (biology) , reliability (semiconductor) , diffusion , mathematical analysis , homotopy , pure mathematics , biochemistry , chemistry , physics , power (physics) , repressor , quantum mechanics , biology , gene , transcription factor , economics , genetics , economic growth , thermodynamics
In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.