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Impulsive fractional partial differential equations

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  • Guo, Tian Liang
  • Zhang, KanJian

Abstract

This paper deals with Cauchy problem for a class of impulsive partial hyperbolic differential equations involving the Caputo derivative. Our first purpose is to show that the formula of solutions in cited papers are incorrect. Next, we reconsider a class of impulsive fractional partial hyperbolic differential equations and introduce a correct formula of solutions for Cauchy problem in Rn. Further, some sufficient conditions for existence of the solutions are established by applying fixed point method. At last, we consider the Cauchy problem in a Banach space via the technique of measures of noncompactness and Mönch’s fixed point theorem. Some examples are given to illustrate our results.

Suggested Citation

  • Guo, Tian Liang & Zhang, KanJian, 2015. "Impulsive fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 581-590.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:581-590
    DOI: 10.1016/j.amc.2014.05.101
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    Cited by:

    1. An, Shujuan & Tian, Kai & Ding, Zhaodong & Jian, Yongjun, 2022. "Electroosmotic and pressure-driven slip flow of fractional viscoelastic fluids in microchannels," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Sun, Yuting & Hu, Cheng & Yu, Juan & Shi, Tingting, 2023. "Synchronization of fractional-order reaction-diffusion neural networks via mixed boundary control," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    3. Asgari, M. & Ezzati, R., 2017. "Using operational matrix of two-dimensional Bernstein polynomials for solving two-dimensional integral equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 290-298.
    4. Wang, Wansheng & Huang, Yi, 2023. "Analytical and numerical dissipativity for the space-fractional Allen–Cahn equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 80-96.
    5. Zhu, Lin & Liu, Nabing & Sheng, Qin, 2023. "A simulation expressivity of the quenching phenomenon in a two-sided space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    6. Kundu, Snehasis, 2018. "Suspension concentration distribution in turbulent flows: An analytical study using fractional advection–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 135-155.
    7. Zhang, Zhi-Yong & Li, Guo-Fang, 2020. "Lie symmetry analysis and exact solutions of the time-fractional biological population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Zhao, Yongqiang & Tang, Yanbin, 2024. "Critical behavior of a semilinear time fractional diffusion equation with forcing term depending on time and space," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    9. Xiaozhong Yang & Lifei Wu, 2020. "A New Kind of Parallel Natural Difference Method for Multi-Term Time Fractional Diffusion Model," Mathematics, MDPI, vol. 8(4), pages 1-19, April.

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