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Study on the mild solution of Sobolev type Hilfer fractional evolution equations with boundary conditions

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  • Gou, Haide
  • Li, Baolin

Abstract

This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of properties of Hilfer fractional calculus, the theory of propagation family as well as the theory of the measure of noncompactness and the fixed point methods, we obtain the existence results of mild solutions for Sobolev type fractional evolution differential equations involving Hilfer fractional derivative. Finally, two examples are presented to illustrate the main result.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:112:y:2018:i:c:p:168-179
    DOI: 10.1016/j.chaos.2018.05.007
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    References listed on IDEAS

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    1. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    2. 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.
    3. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
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    Cited by:

    1. Vijayakumar, V. & Udhayakumar, R., 2020. "Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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