Analysis of some dynamical systems by combination of two different methods

Area of Science:

• Applied Mathematics
• Fractional Calculus
• Numerical Analysis

Background:

• Partial differential equations (PDEs) are fundamental in modeling complex phenomena.
• Fractional derivatives, like the Caputo derivative, are crucial for systems exhibiting memory and non-local behaviors.
• Existing methods may face challenges in efficiently solving PDEs with fractional orders.

Purpose of the Study:

• To introduce a novel iterative method for solving systems of PDEs with Caputo derivatives.
• To leverage the Elzaki transformation to enhance the efficiency of the iterative approach.
• To provide accurate and efficient solutions for fractional dynamics.

Main Methods:

• A novel iterative method is developed.
• The Elzaki transformation is integrated into the iterative scheme.
• Numerical experiments are conducted for validation.

Main Results:

• The proposed method effectively solves systems of PDEs involving Caputo derivatives.
• Numerical results demonstrate the accuracy and efficiency of the Elzaki-transform-based iterative technique.
• The method successfully handles intricate fractional dynamics.

Conclusions:

• The Elzaki-transform-based iterative method is a versatile tool for fractional PDEs.
• The study contributes to the application of fractional calculus in solving complex mathematical systems.
• The developed technique shows potential for various scientific and engineering applications.