Modified conformable double Laplace-Sumudu approach with applications

Area of Science:

• Mathematics
• Applied Mathematics
• Numerical Analysis

Background:

• Nonlinear fractional partial differential equations (NFPDEs) are crucial in modeling complex phenomena.
• Existing analytical and numerical methods often face challenges in solving NFPDEs.
• Novel techniques are needed for efficient and accurate solutions of NFPDEs.

Purpose of the Study:

• To introduce a new hybrid method, the conformable double Laplace-Sumudu modified decomposition (CDLSMD) method.
• To solve nonlinear fractional partial differential equations using the CDLSMD method.
• To demonstrate the essential properties of the conformable double Laplace-Sumudu transform (CDLST) and derive new results.

Main Methods:

• Combining the conformable double Laplace-Sumudu transform (CDLST) with the modified decomposition technique.
• Developing the conformable double Laplace-Sumudu modified decomposition (CDLSMD) method.
• Applying the CDLSMD method to solve nonlinear fractional partial differential equations.

Main Results:

• The study presents essential properties and new results for the CDLST.
• The CDLSMD method is applied to five illustrative examples.
• The efficiency and applicability of the CDLSMD method are demonstrated through these examples.

Conclusions:

• The CDLSMD method is a powerful and effective technique for solving NFPDEs.
• The proposed method shows significant strength in addressing various types of problems.
• The findings contribute to the advancement of numerical methods for fractional calculus.