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

Kamal Shah (), Zamin Gul (), Yongjin Li () and Rahmat Ali Khan ()
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Kamal Shah: University of Malakand, Department of Mathematics
Zamin Gul: University of Malakand, Department of Mathematics
Yongjin Li: Sun Yat-sen University, Department of Mathematics
Rahmat Ali Khan: University of Malakand, Department of Mathematics

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 45-71 from Springer

Abstract: 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.

Keywords: Nonlinear FDEs; Fixed point; BVPs; Stability results; 26A33; 34A08; 35B40 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28950-8_3

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DOI: 10.1007/978-3-030-28950-8_3

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