ANALYTICAL SOLUTIONS AND EFFICIENT COMPACT SCHEMES OF THE CAPUTO-HADAMARD TIME FRACTIONAL MODEL FOR NANOFLUID

Shujun Shen; Guocai Cai; Qingxia Liu

doi:10.11948/20260022

2027 Volume 17 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2027 > 17(3): 1696-1723

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Shujun Shen, Guocai Cai, Qingxia Liu. ANALYTICAL SOLUTIONS AND EFFICIENT COMPACT SCHEMES OF THE CAPUTO-HADAMARD TIME FRACTIONAL MODEL FOR NANOFLUID[J]. Journal of Applied Analysis & Computation, 2027, 17(3): 1696-1723. doi: 10.11948/20260022

Citation:

Shujun Shen, Guocai Cai, Qingxia Liu. ANALYTICAL SOLUTIONS AND EFFICIENT COMPACT SCHEMES OF THE CAPUTO-HADAMARD TIME FRACTIONAL MODEL FOR NANOFLUID[J]. Journal of Applied Analysis & Computation, 2027, 17(3): 1696-1723. doi: 10.11948/20260022

ANALYTICAL SOLUTIONS AND EFFICIENT COMPACT SCHEMES OF THE CAPUTO-HADAMARD TIME FRACTIONAL MODEL FOR NANOFLUID

1.
Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, China
2.
School of Mathematical Sciences, Xiamen University, Xiamen, China
3.
Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian, China

Author Bio: Email: shensj12@sina.com(S. Shen)
Corresponding authors: Email: gotry@xmu.edu.cn(G. Cai); Email: liuqx@xmu.edu.cn(Q. Liu)
Fund Project: The authors were supported by Fujian Provincial Natural Science Foundation of China (Grant No. 2026J001045) and the National Natural Science Foundation of China (Grant Nos. 12371372, 12371081 and 12271450)

Abstract

Abstract

In this paper, we consider the Caputo-Hadamard time fractional model for unsteady MHD mixed convection problem of Maxwell fractional nanofluid. Two kinds of boundary conditions are proposed, which are Dirichlet boundary conditions and Robin boundary conditions. The analytical solutions for the equation are derived by using the method of separation of variables and the generalized Laplace transform. The numerical schemes are developed based on the L1 and L1-2 approximations for the Caputo-Hadamard fractional derivatives and the compact finite difference scheme for spatial derivative. Stability and convergence of the obtained numerical scheme are analyzed theoretically. Numerical examples are constructed to demonstrate the accuracy of the numerical scheme as compared to theoretical analysis.
- Caputo-Hadamard /
- analytical solution /
- separation of variables /
- generalized Laplace transform /
- compact scheme
MSC: 35R11, 65M06, 65Mxx

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References

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