Existence and uniqueness results for positive solutions of Hadamard type fractional BVP

References

• I. Podlubny : Fractional Differential Equations, Academic Press, San Diego, (1999).
   Google Scholar
• J. Hadamard : Essai sur ietude des fonctions donnees par leur developpment de taylor, J. Math. Pures Appl. Ser., 8, 101-186 (1892).
   Google Scholar
• A. A. Kilbas, H. M. Srivastava, J. J. Trujillo : Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, (2006).
   Google Scholar
• R. P. Agarwal, D. O’ Regan, S. Stank : Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. Math. Anal. Appl., 371, 57-68 (2010). doi: 10.1016/j.jmaa.2010.04.034
   Web of Science ®Google Scholar
• Z. B. Bai, H. S. L : Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311, 495-505 (2005). doi: 10.1016/j.jmaa.2005.02.052
   Web of Science ®Google Scholar
• X. Zhang, L. Liu, Y. Wu, : Multiple positive solutions of a singular fractional differential equation with negatively perturbed term. Math. Comput. Model., 55, 1263-1274 (2012). doi: 10.1016/j.mcm.2011.10.006
   Google Scholar
• Y. Qiao, Z. Zhou ; Existence and uniqueness of positive solutions for a fractional differential equation with integral boundary conditions Adv. Differ. Equ., 106, 1-18 (2016).
   Google Scholar
• P. Thiramanus, S.K. Ntouyas, J. Tariboon : Positive solutions for Hadamard fractional differential equations on infinite domain, Adv. Differ. Equ., 83, 1-18 (2016).
   Google Scholar
• W. Yang, Y. Qin, Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions, ScienceAsia, 43, 201-206 (2017). doi: 10.2306/scienceasia1513-1874.2017.43.201
   Web of Science ®Google Scholar
• C. B. Zhai, D. R. Anderson : A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations. J. Math. Anal. Appl., 375, 388-400 (2011). doi: 10.1016/j.jmaa.2010.09.017
   Web of Science ®Google Scholar
• C. Yang, C. Zhai, M. Hao : Uniqueness of positive solutions for several classes of sum operator equations and applications, J. Inequal. Appl., 58 (2014).
   Google Scholar
• J. Wang, Y. Zhou, M. Medved : Existence and stability of fractional differential equations with Hadamard derivative, Topol. Methods Nonlinear Anal., 41, 113-133 (2013).
   Web of Science ®Google Scholar
• B. Ahmad and S. K. Ntouyas : On Hadamard fractional integro-differential boundary value problems, Journal of Applied Mathematics and Computing, 47, 119-131 (2015). doi: 10.1007/s12190-014-0765-6
   Web of Science ®Google Scholar
• C. Zhai, D. R. Anderson : A sum operator equation and applications to nonlinear elastic beam equations and LaneEmdenFowler equations; Journal of Mathematical Analysis and Applications; 375 : 2, 388-400 (2011). doi: 10.1016/j.jmaa.2010.09.017
   Web of Science ®Google Scholar
• U. Witthayarat, K. Wattanawitoon, P. Kumam : Iterative Scheme for System of Equilibrium Problems and Bregman Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces, Journal of Information and Optimization Sciences, 37:3, 321-342, DOI: 10.1080/02522667.2014.932093 (2016).
   Web of Science ®Google Scholar
• K. Qiu, J. R. Wang : A fractional integral identity and its application to fractional Hermite-Hadamard type inequalities, Journal of Interdisciplinary Mathematics, 21:1, 1-16, DOI: 10.1080/09720502.2017.1400795 (2018).
   Web of Science ®Google Scholar
• M. W. Mohammad, D. Maslina, S. K. Ugur : Some inequalities of Hermite-Hadmard type for s-convex functions, Acta Math. Sci., 31B, 1643-1652 (2011).
   Google Scholar
• M. Z. Sarikaya, E. Set, H. Yaldiz, N. Bak : Hermite-Hadamards inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57, 2403-2407 (2013). doi: 10.1016/j.mcm.2011.12.048
   Web of Science ®Google Scholar
• A. J. B. Potter: Applications of Hilberts projective metric to certain classes of non-homogenous operators. Quart. J. Math. Oxford Ser., 28(2), 93-99 (1977). doi: 10.1093/qmath/28.1.93
   Google Scholar