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The fundamental solutions for fractional evolution equations of parabolic type

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  • Mahmoud M. El-Borai

Abstract

The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

Suggested Citation

  • Mahmoud M. El-Borai, 2004. "The fundamental solutions for fractional evolution equations of parabolic type," International Journal of Stochastic Analysis, Hindawi, vol. 2004, pages 1-15, January.
    • Handle: RePEc:hin:jnijsa:484863
    DOI: 10.1155/S1048953304311020
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    Cited by:

    1. Ge, Fudong & Chen, YangQuan, 2017. "Extended Luenberger-type observer for a class of semilinear time fractional diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 229-235.
    2. Gou, Haide & Li, Baolin, 2018. "Study on the mild solution of Sobolev type Hilfer fractional evolution equations with boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 168-179.

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