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- Title
Numerical Solution of Nonlinear Fractional Diffusion Equation in Framework of the Yang-Abdel-Cattani Derivative Operator.
- Authors
Malyk, Igor V.; Gorbatenko, Mykola; Chaudhary, Arun; Sharma, Shivani; Dubey, Ravi Shanker
- Abstract
In thismanuscript, the time-fractional diffusion equation in the framework of the Yang-Abdel-Cattani derivative operator is taken into account. A detailed proof for the existence, as well as the uniqueness of the solution of the time-fractional diffusion equation, in the sense of YAC derivative operator, is explained, and, using the method of a-HATM, we find the analytical solution of the timefractional diffusion equation. Three cases are considered to exhibit the convergence and fidelity of the aforementioned a-HATM. The analytical solutions obtained for the diffusion equation using the Yang-Abdel-Cattani derivative operator are compared with the analytical solutions obtained using the Riemann-Liouville (RL) derivative operator for the fractional order g = 0.99 (nearby 1) and with the exact solution at different values of t to verify the efficiency of the YAC derivative operator.
- Subjects
BOUNDARY value problems; EIGENFUNCTIONS; NUMERICAL solutions to boundary value problems; MATHEMATICAL analysis; NUMERICAL solutions for linear algebra
- Publication
Fractal & Fractional, 2021, Vol 5, Issue 3, p1
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract5030064