A new analysis for the Keller-Segel model of fractional order. (English) Zbl 1365.65233
Summary: In this study, we discuss the application of an analytical technique namely modified homotopy analysis transform method (MHATM) for solving coupled one- dimensional time-fractional Keller-Segel (K-S) equations [E. F. Keller and L. A. Segel, J. Theor. Biol. 26, No. 3, 399–415 (1970; Zbl 1170.92306)]. The MHATM is a new analytical technique based on homotopy polynomial. We provide a convergence analysis of MHATM and the solution obtained by the proposed method is verified through different graphical representations. The results demonstrate that the proposed methodology is very useful and simple in the determination of the solution of the K-S equations of fractional order.
MSC:
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35R11 | Fractional partial differential equations |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
Keller- Segel equation; homotopy polynomial; convergence; homotopy analysis transform method numerical examples; convergence; fractional orderCitations:
Zbl 1170.92306References:
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