Uniqueness of solutions for boundary value problems for nonlinear fractional differential equations
DOI:
https://doi.org/10.12775/TMNA.2024.036Słowa kluczowe
Fractional differential equation, uniqueness of solutions, first eigenvalue, u_0-positive, Banach's contraction mapping principleAbstrakt
In this paper, we investigate uniqueness of solutions for a type of nonlinear fractional differential equations with integral boundary conditions. Different from most existing results, we use three new methods to get the uniqueness results. Specifically, we respectively utilize Banach's contraction mapping principle, linear operator theory and $u_{0}$-positive operators.Bibliografia
R.P. Agarwal, B. Mouffak and H. Samira, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109 (2010), 973–1033.
B. Ahmad and J.J. Nieto, Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray–Schauder degree theory, Topol. Methods Nonlinear Anal. 35 (2010), 295–304.
B. Ahmad, S.K. Ntouyas and A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Difference Equ. 2011 (2011), ID 107384.
A. Cabada and Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput. 228 (2014), 251–257.
A. Cabada and G.T. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Math. Anal. Appl. 389 (2012), 403–411.
Y.J. Cui, Uniqueness of solution for boundary value problems for fractional differential equations, Appl. Math. Lett. 51 (2016), 48–54.
Y.J. Cui, W.J. Ma, Q. Sun and X.W. Su, New uniqueness results for boundary value problem of fractional differential equation, Nonlinear Anal.-Model. 23 (2018), 31–39.
D.B. Dhaigude, V.S. Gore and P.D. Kundgar, Existence and uniqueness of solution of nonlinear boundary value problems for ψ-Caputo fractional differential equations, Malaya J. Mat. 9 (2021), 112–117.
Y.H. Duan and W.X. Wang, The existence and uniqueness of positive solutions for a class of boundary value problems of arbitrary fractional order differential equations with deviated arguments, J. Cent. China Norm. Univ. Nat. Sci. 56 (2022), 567–576.
X.L. Han, H.Z Cai and H.J. Yang, Existence and uniqueness of solutions for the boundary value problems of nonlinear fractional differential equations on star graph, Acta Math. Sci. Ser. A (Chin. Ed.) 56 (2022), 567–576.
A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.
M.A. Krasnosel’skiı̆, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, 1964.
A. Lachouri, A. Ardjouni and A. Djoudi, Existence and uniqueness of mild solutions of boundary value problems for Caputo–Hadamard fractional differential equations with integral and anti-periodic conditions, J. Fract. Calc. Appl. 12 (2021), 60–68.
S. Li, Z.X. Zhang and W. Jiang, Existence and uniqueness of solutions for boundary value problems of fractional differential equations with delay, Gongcheng Shuxue Xuebao 38 (2021), 700–708.
K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1993.
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198, Academic Press, Inc., San Diego, CA, 1999.
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993.
C.B. Zhai, C. Yang and X.Q. Zhang, Positive solutions for nonlinear operator equations and several classes of applications, Math. Z. 266 (2010), 43–63.
C.B. Zhai and F. Wang, Properties of positive solutions for the operator equation Ax = λx and applications to fractional differential equations with integral boundary conditions, Adv. Difference Equ. 2015 (2015), 1–10.
C.B. Zhai and L. Wang, Pφ-(h, e)-concave operators and applications, J. Math. Anal. Appl. 454 (2017), 571–584.
X.H. Zhang, L.S. Liu and Y.H. Wu, Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math. Comput. Modelling 55 (2012), 1263–1274.
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