A hybrid yang transform adomian decomposition method for solving time-fractional nonlinear partial differential...

Area of Science:

• Numerical Analysis
• Applied Mathematics
• Fractional Calculus

Background:

• Nonlinear time-fractional partial differential equations (NTFPDEs) are crucial for modeling diverse real-world systems.
• Solving NTFPDEs presents significant challenges due to nonlinearities and fractional operators.
• Developing efficient numerical methods for NTFPDEs is an active research domain.

Purpose of the Study:

• To introduce a novel numerical technique, the Yang transform Adomian decomposition method (YTADM).
• To apply YTADM for solving nonlinear time-fractional partial differential equations (NTFPDEs) using the Caputo fractional derivative.
• To analyze the stability and convergence properties of the developed YTADM.

Main Methods:

• The study integrates the Yang transform with the Adomian decomposition method.
• The Caputo fractional derivative is employed to handle fractional orders.
• Stability and convergence are rigorously analyzed within the Banach space framework.

Main Results:

• The proposed Yang transform Adomian decomposition method (YTADM) is demonstrated to be effective and practical.
• YTADM provides accurate solutions for nonlinear time-fractional partial differential equations.
• The method shows superior performance compared to existing numerical techniques.

Conclusions:

• The developed YTADM is a robust and efficient numerical tool for NTFPDEs.
• The method achieves high accuracy with a minimal number of iterations.
• YTADM is well-suited for applications involving complex nonlinear phenomena modeled by fractional differential equations.