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Existence of mild solution for evolution equation with Hilfer fractional derivative

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  • Gu, Haibo
  • Trujillo, Juan J.

Abstract

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:344-354
    DOI: 10.1016/j.amc.2014.10.083
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    References listed on IDEAS

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    1. Yan, Jianping & Li, Changpin, 2007. "On chaos synchronization of fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 725-735.
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    Cited by:

    1. Sivajiganesan Sivasankar & Ramalingam Udhayakumar, 2022. "Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(12), pages 1-19, June.
    2. B. Radhakrishnan & T. Sathya, 2022. "Controllability of Hilfer Fractional Langevin Dynamical System with Impulse in an Abstract Weighted Space," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 265-281, October.
    3. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Velmurugan Subramanian & Ghada AlNemer & Ahmed M. Elshenhab, 2022. "Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(22), pages 1-18, November.
    4. Boudjerida, Assia & Seba, Djamila, 2021. "Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    6. Yao-Qun Wu & Jia Wei He, 2022. "Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 79-101, October.
    7. Ahmed, Hamdy M. & El-Borai, Mahmoud M., 2018. "Hilfer fractional stochastic integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 182-189.
    8. Ahmed, Hamdy M. & Zhu, Quanxin, 2023. "Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise," Statistics & Probability Letters, Elsevier, vol. 195(C).
    9. Nisar, Kottakkaran Sooppy & Jothimani, K. & Kaliraj, K. & Ravichandran, C., 2021. "An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Muchenedi Hari Kishor & Sharifah E. Alhazmi & Shrideh Al-Omari, 2022. "A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    11. 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.
    12. Sousa, J. Vanterler da C. & Oliveira, D.S. & Capelas de Oliveira, E., 2021. "A note on the mild solutions of Hilfer impulsive fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    13. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    14. Athasit Wongcharoen & Sotiris K. Ntouyas & Jessada Tariboon, 2020. "Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-11, October.
    15. Nawapol Phuangthong & Sotiris K. Ntouyas & Jessada Tariboon & Kamsing Nonlaopon, 2021. "Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    16. Yong Zhou, 2022. "Infinite Interval Problems for Fractional Evolution Equations," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    17. 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).
    18. Surang Sitho & Sotiris K. Ntouyas & Ayub Samadi & Jessada Tariboon, 2021. "Boundary Value Problems for ψ -Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    19. Guotao Wang & Jianfang Qin & Huanhe Dong & Tingting Guan, 2019. "Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System," Mathematics, MDPI, vol. 7(6), pages 1-10, June.

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