Existence results for positive solutions of a fractional boundary value problem involving a perturbation term
Keywords:
Fractional differential equations, admissible mappings, perturbation term, ower positive solution, F -metric spacesAbstract
A new fixed-point result criteria for the existence of positive solutions to the considered problem are established based on upper and lower estimates and \(\alpha\)-admissible mappings in \(F\)-metric spaces for Green's function related to a fractional boundary value problem with a perturbation term, which has been derived.
References
H. Afshari, A. Ahmadkhanlu, A discussion on some new boundary value problems involving the $q$-derivative operator via the existence of positive solutions. Opt. Quantum Electron. 56, 1312 (2024). https://doi.org/10.1007/s11082-024-07189-7
H. Afshari, A. Ahmadkhanlu, The existence of positive solutions for a Caputo–Hadamard boundary value problem with an integral boundary condition. Adv. Theory Nonlinear Anal. Appl. 7(5), 155–164 (2023). https://doi.org/10.17762/atnaa.v7.i5.332
H. Afshari, M. Nosrati Sahlan, The existence of solutions for some new boundary value problems involving the q-derivative operator in quasi-b-metric and b-metric-like spaces, Letters in Nonlinear Analysis and its Applications 2 (2024) No. 1, 16-22.
A. Pourgholam, and H. Afshari, (2024). New areas of fixed point results for multi-valued mappings and its applications. Mathematics and Computational Sciences, 4(4), 1-9. doi: 10.30511/mcs.2023.2011791.1140
V. Roomi, H. Afshari, M. Nosrati, Existence and uniqueness for a fractional differential equation involving Atangana-Baleanu derivative by using a new contraction,
Letters in Nonlinear Analysis and its Application, 1 (2) (2023), 52–56.
Z. Bai, SH. Zhang, S. Sun, Ch. Yin, Monotone iterative method for a class of fractional differential equations, Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 06, pp. 1-8.
Z. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Analysis, (72)2010: 916-924.
A. Cabada, Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput., 228(2014),251-257.
Y. Cui, Uniqueness of solution for boundary value problems for fractional differential equations, Applied Mathematics Letters, 51(2016)48-54.
Y. Cui, W. Ma, Q. Sun, X. Su, New uniqueness results for boundary value problem of fractional differential equation, Nonlinear Anal. Model. Control, 23(2018), 31-39.
O. Popescu,textit{Some new fixed point theorems for $alpha-$Geraghty-contraction type maps in metric spaces.} Fixed Point Theory Appl. (2014), 2014:190.
Y. Cui, W. Ma, X. Wang, X. Su, Uniqueness theorem of differential system with coupled integral boundary conditions, Electron. J. Qual. Theory Differ. Equ. 2018, No. 9, 1-10.
M. El-Shahed, Positive solutions for boundary value problem of nonlinear fractional differential equation, Abs. Appl. Anal., Volume 2007, Article ID 10368.
J. R. Graef, L, Kong, Q. Kong, M. Wang, On a fractional boundary value problem with a perturbation term, Journal of Applied Analysis and Computation, 2017(7):57-66
X. Hao, Positive solution for singular fractional differential equations involving derivatives, Advances in Difference Equations (2016) 2016: 139.
X. Hao, H. Wang, L. Liu, Y. Cui, Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and $p$-Laplacian operator, Boundary Value Problems, (2017) 2017: 182.
L. Liu, F. Sun, X. Zhang, Y. Wu, Bifurcation analysis for a singular differential system with two parameters via to degree theory, Nonlinear Anal. MC, 22(1)(2017), 31-50.
Q. Sun, H. Ji, Y. Cui, Positive solutions for boundary value problems of fractional differential equation with integral boundary conditions, Journal of Function Spaces, Volume 2018 (2018), Article ID 6461930, 6 pages.
Jleli M., Samet B., On a new generalization of metric spaces, Fixed Point Theory Appl. (2018)textbf{ 2018}: 128.
F. Yan, M. Zuo, X. Hao, Positive solution for a fractional singular boundary value problem with $p$-Laplacian operator, Boundary Value Problems, (2018) 2018: 51.
H. Aydi, E. Karapinar, ZD. Mitrovi, T. Rashid, A remark on "Existence and uniqueness for a neutral differential problem with unbo unded delay via fixed point results F-metric space", RACSAM, doi:org/10.1007/s13398-019-00690-9.
X. Zhang, Q. Zhong, Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions, Fract. Calc. Appl. Anal., 20 (6) (2017)1471-1484.
X. Zhang, Q. Zhong, Triple positive solutions for nonlocal fractional differential equations with singularities both on time and space variables, Appl. Math. Lett. 80 (2018) 12-19.
Y. Zou, G. He, A fixed point theorem for systems of nonlinear operator equations and applications to $(p_1,p_2)$-Laplacian system, Mediterr. J. Math.(2018) 15:74
A. Amini-Harandi, H. emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010), 2238–2242
M. Zuo, X. Hao, L. Liu, Y. Cui, Existence results for impulsive fractional integro-differential equation of mixed type with constant coeffcient and antiperiodic boundary conditions, Boundary Value Problems (2017) 2017:161.
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