New Method for Solving Nonlinear Partial Fractional Differential Equations
Author Information
Author(s): Khan Zareen A., Riaz Muhammad Bilal, Liaqat Muhammad Imran, Akgül Ali
Primary Institution: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
Hypothesis
Can a novel technique combining integral transforms and residual functions effectively solve nonlinear partial fractional differential equations?
Conclusion
The proposed method demonstrates high accuracy and effectiveness in solving various nonlinear problems within the Caputo derivative framework.
Supporting Evidence
- The method provides both approximate and exact solutions for various nonlinear problems.
- The results show high agreement with existing methods, validating the effectiveness of the new approach.
- The technique can handle nonlinear problems without relying on traditional polynomial methods.
- The study highlights the advantages of using the Elzaki transform in solving fractional differential equations.
Takeaway
This study introduces a new way to solve complex math problems that involve fractions, making it easier to find answers that are usually hard to get.
Methodology
The study employs a novel technique called the Elzaki residual approach, which combines the Elzaki transform with modified fractional power series and residual functions.
Limitations
The method requires the source functions to be piecewise continuous and of exponential order, and assumes the Caputo derivative adheres to the semigroup property.
Digital Object Identifier (DOI)
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