Abstract
In this paper, we study the existence of positive solutions for a class of nonlinear fractional boundary value problems with integral boundary conditions in Hölder spaces. Our analysis relies on a sufficient condition for the relative compactness in Hölder spaces and the classical Schauder fixed point theorem.
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References
Ahmad, B., Nieto, J.J., Alsaedi, A., El-Shahed, M.: A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Anal. Real World Appl. 13(2), 599–606 (2012)
Al-Refai, M., Hajji, M.A.: Monotone iterative sequences for nonlinear boundary value problems of fractional order. Nonlinear Anal. 74(11), 3531–3539 (2011)
Banaś, J., Nalepa, R.: On the space of functions with growths tempered by a modulus of continuity and its applications. J. Funct. Spaces Appl. 2013, (2013). doi:10.1155/2013/820437
Cabada, A., Wang, G.: Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J. Math. Anal. Appl. 389(1), 403–411 (2012)
Caballero, J., López, B., Sadarangani, K.: On monotonic solutions of an integral equation of Volterra type with supremum. J. Math. Anal. Appl. 305(1), 304–315 (2005)
Caballero, J., Harjani, J., Sadarangani, K.: On existence and uniqueness of positive solutions to a class of fractional boundary value problems. Bound. Value Probl. 2011, 25 (2011)
Caballero, J., Darwish, M.A., Sadarangani, K.: Solvability of a quadratic integral equation of Fredholm type in Hölder spaces. Electron. J. Differ. Equ. 31, 1–10 (2014)
Chen, J., Tang, X.H.: Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory. Abstr. Appl. Anal. 2012, (2012). doi:10.1155/2012/648635
Jankowski, T.: Fractional problems with advanced arguments. Appl. Math. Comput. 230, 371–382 (2014)
Jiao, F., Zhou, Y.: Existence of solutions for a class of fractional boundary value problems via critical point theory. Comput. Math. Appl. 62(3), 1181–1199 (2011)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V., Amsterdam (2006)
Pei, K., Wang, G., Sun, Y.: Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain. Appl. Math. Comput. 312, 158–168 (2017)
Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon & Breach, Yverdon (1993)
Su, X.: Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett. 22(1), 64–69 (2009)
Wang, G.: Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments. J. Comput. Appl. Math. 236(9), 2425–2430 (2012)
Yu, Y., Jiang, D.: Multiple Positive Solutions for the Boundary Value Problem of A Nonlinear Fractional Differential Equation. Northeast Normal University, Changchun (2009)
Zhang, L., Ahmad, B., Wang, G.: Successive iterations for positive extremal solutions of nonlinear fractional differential equations on a half-line. Bull. Aust. Math. Soc. 91(1), 116–128 (2015)
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Caballero, J., Darwish, M.A. & Sadarangani, K. Positive Solutions in the Space of Lipschitz Functions for Fractional Boundary Value Problems with Integral Boundary Conditions. Mediterr. J. Math. 14, 201 (2017). https://doi.org/10.1007/s00009-017-1001-z
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DOI: https://doi.org/10.1007/s00009-017-1001-z