Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = α-homotopy analysis transform method

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
12 pages, 2371 KB  
Article
Numerical Solution of Nonlinear Fractional Diffusion Equation in Framework of the Yang–Abdel–Cattani Derivative Operator
by Igor V. Malyk, Mykola Gorbatenko, Arun Chaudhary, Shivani Sharma and Ravi Shanker Dubey
Fractal Fract. 2021, 5(3), 64; https://doi.org/10.3390/fractalfract5030064 - 2 Jul 2021
Cited by 25 | Viewed by 3084
Abstract
In this manuscript, 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 [...] Read more.
In this manuscript, 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 α-HATM, we find the analytical solution of the time-fractional diffusion equation. Three cases are considered to exhibit the convergence and fidelity of the aforementioned α-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 γ=0.99 (nearby 1) and with the exact solution at different values of t to verify the efficiency of the YAC derivative operator. Full article
Show Figures

Figure 1

Back to TopTop