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An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations
Ravi P Agarwal1, Fatemah Mofarreh2, Rasool Shah3
1Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA.
Entropy (Basel, Switzerland)
|August 27, 2021
Summary
This study introduces a new analytical method combining the Adomian decomposition method and natural transform to solve fractional-order parabolic equations, offering accurate closed-form solutions.
Area of Science:
- Numerical analysis
- Applied mathematics
- Fractional calculus
Background:
- Fractional-order parabolic equations present significant challenges in analytical solutions.
- Existing numerical methods may lack accuracy or efficiency for these complex equations.
Purpose of the Study:
- To develop and present an innovative analytical technique for solving fractional-order parabolic equations.
- To establish closed-form solutions for targeted fractional-order differential equations.
Main Methods:
- The Adomian decomposition method (ADM) is integrated with the natural transform (NT).
- This combined approach, NT-ADM, is applied to derive analytical solutions.
Main Results:
- The proposed NT-ADM technique successfully provides closed-form solutions for fractional-order parabolic equations.
- Graphical analysis confirms the accuracy of the obtained solutions, showing good agreement with exact solutions.
- Solutions for fractional orders were observed to converge towards the solutions of integer-order problems.
Conclusions:
- The NT-ADM is an accurate, simple, and effective method for solving fractional-order parabolic equations.
- This technique offers a valuable alternative to existing methods, providing straightforward closed-form solutions.
- The method has potential for application to a broader range of fractional-order partial differential equations.
Keywords:
Caputo–Fabrizio operatorfractional-order parabolic equationsnatural transform decomposition methodMore Related Videos
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