Nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions and Ulam–Hyers stability

被引：0
作者：
Fang Li
Wenjing Yang
Huiwen Wang
机构：
[1] Yunnan Normal University,School of Mathematics
来源：
Boundary Value Problems | / 2020卷
关键词：
Mixed fractional derivatives; Nonlocal boundary value problem; Mittag-Leffler function; Ulam–Hyers stability; 34A08; 34A37; 34B10;
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学科分类号：
摘要：
In this paper, we study a nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions. By using some new techniques, we introduce a formula of solutions for above problem, which can be regarded as a novelty item. Moreover, under the weak assumptions and using Leray–Schauder degree theory, we obtain the existence result of solutions for above problem. Furthermore, we discuss the Ulam–Hyers stability of the above fractional differential equation. Three examples illustrate our results.
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  • [1] Agrawal O.P.(2010)Generalized variational problems and Euler–Lagrange equations Comput. Math. Appl. 59 1852-1864
  • [2] Atanackovic T.M.(2007)On a differential equation with left and right fractional derivatives Fract. Calc. Appl. Anal. 10 139-150
  • [3] Stankovic B.(2015)Fractional oscillator equation—transformation into integral equation and numerical solution Appl. Math. Comput. 257 428-435
  • [4] Blaszczyk T.(2017)Condensing operators and periodic solutions of infinite delay impulsive evolution equations Discrete Contin. Dyn. Syst., Ser. S 10 475-485
  • [5] Ciesielski M.(2019)Solutions to fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions Banach J. Math. Anal. 13 745-768
  • [6] Liang J.(2018)Three nontrivial solutions for nonlinear fractional Laplacian equations Adv. Nonlinear Anal. 7 211-226
  • [7] Liu J.H.(2019)A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications Adv. Nonlinear Anal. 8 386-454
  • [8] Xiao T.J.(2019)Periodic impulsive fractional differential equations Adv. Nonlinear Anal. 8 482-496
  • [9] Liang J.(2016)Solvability of a boundary value problem at resonance SpringerPlus 5 2220-2240
  • [10] Mu Y.(1941)On the stability of the linear functional equation Proc. Natl. Acad. Sci. 27 5-17
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