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Hyers–Ulam’s Stability Results to a Three-Point Boundary Value Problem of Nonlinear Fractional Order Differential Equations

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Frontiers in Functional Equations and Analytic Inequalities

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Abstract

This research is devoted to investigate the existence and multiplicity results of boundary value problem (BVP) for nonlinear fractional order differential equation (FDEs). To obtain the required results, we use some fixed point theorems due to Leggett–Williams and Banach. Further in this paper, we introduce different types of Ulam’s stability concepts for the aforesaid problem of nonlinear FDEs. The concerned types of Ulam’s stability are devoted to Ulam–Hyers (UH), generalized Ulam–Hyers (GUH) stability and Ulam–Hyers–Rassias (UHR), generalized Ulam–Hyers–Rassias (GUHR) stability. Finally the whole analysis is verified by some adequate examples.

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Acknowledgements

The authors declare that there does not exist any conflict of interest. Further, this work has been supported by the National Natural Science Foundation of China (11571378).

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Authors and Affiliations

  1. Department of Mathematics, University of Malakand, Chakadara Dir (L), Khyber Pakhtunkhwa, Pakistan

    Kamal Shah, Zamin Gul & Rahmat Ali Khan

  2. Department of Mathematics, Sun Yat-sen University, Guangzhou, China

    Yongjin Li

Authors
  1. Kamal Shah
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  2. Zamin Gul
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  3. Yongjin Li
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  4. Rahmat Ali Khan
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Corresponding author

Correspondence to Yongjin Li .

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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Shah, K., Gul, Z., Li, Y., Khan, R.A. (2019). Hyers–Ulam’s Stability Results to a Three-Point Boundary Value Problem of Nonlinear Fractional Order Differential Equations. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_3

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