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Pure Mathematics 2023
Tempered分数阶微分方程Nagumo型唯一解
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Abstract:
本文重点讨论Tempered分数阶微分方程柯西问题Nagumo迭代近似值的唯一性和收敛性。首先把柯西问题转化成等价Volterra积分方程，证出解的唯一性。然后，运用迭代方法，我们将Nagumo型唯一性和迭代近似值序列扩展到Tempered分数阶微分方程。
This work is concerned with Nagumo-type uniqueness and convergence of successive approxima-tions to Cauchy problem for Tempered fractional differential equations. Firstly, to prove the uniqueness of the solution, the Cauchy problem is transformed into an equivalent Volterra integral equation. Then, using the iterative method, we extend Nagumo-type uniqueness and convergence of successive approximations to Tempered fractional differential equations.
| [1] | Podlubny, I. (1999) Fractional Differential Equations. Academic Press, San Diego. |
| [2] | Samko, S., Kilbas, A. and Marichev, O. (1993) Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Lon-don. |
| [3] | Hilfer, R. (2000) Applications of Fractional Calculus in Physics. World Scientific, Singapore.
https://doi.org/10.1142/3779 |
| [4] | Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993) Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, Switzerland, Philadelphia. |
| [5] | Diethelm, K. (2004) The Analysis of Fractional Differential Equations. Journal of Mathematical Analysis and Applications, 256, 229-248. |
| [6] | Buschman, R.G. (1972) Decomposition of an Integral Operator by Use of Mikusinski Calculus. SIAM Journal on Mathematical Analysis, 3, 83-85. https://doi.org/10.1137/0503010 |
| [7] | Chu, J. and Wang, Z. (2023) Nagumo-Type Uniqueness and Stability for Nonlinear Differential Equations on Semi-Infinite Intervals. Journal of Differential Equations, 367, 229-245. https://doi.org/10.1016/j.jde.2023.05.001 |
| [8] | Baeumera, B. and Meerschaert, M. (2010) Tempered Stable Levy Motion and Transient Super-Diffusion. Journal of Computational and Applied Mathematics, 233, 2438-2448. https://doi.org/10.1016/j.cam.2009.10.027 |
| [9] | Cartea, A. and del-Castillo-Negrete, D. (2007) Fluid Limit of the Continuous-Time Random Walk with General Levy Jump Distribution Functions. Physical Review E, 76, Article ID: 041105. https://doi.org/10.1103/PhysRevE.76.041105 |
| [10] | Li, C., Deng, W. and Zhao, L. (2015) Well-Posedness and Numerical Algorithm for the Tempered Fractional Ordinary Differential Equations. arXiv:1501.00376. |
