Nonlinear Boundary Value Problem of Fractional Differential Equations with Arguments under Integral Boundary Condition
In this paper, we develop the existence and uniqueness theory of fractional differential equation involving Riemann-Liouville di¤erential operator of order 0 < < 1, with advanced argument under integral boundary condition. We show the uniqueness of solution by using Banach xed point theorem with a weighted norm. We apply the comparison result and obtain the existence and uniqueness of solution by monotone iterative technique also by use weakly coupled extremal solution of (1.1).
T. A. Burton, Di¤erential inequalities and existence theory for differential, integral, and delay equations, Lecture Notes in Pure and Appl. Math. 1994.
J. V. Devi, F. A. McRae and Z. Drici, Variational Lyapunov Method for Fractional Differential Equations, Comp. Math. Appl. 64 (2012), 2982-2989.
D. B. Dhaigude and B. H. Rizqan, Existence and uniqueness of solutions for fractional differential equations with advanced arguments, Adv. Math. Models & Appl. 2 (3) (2017), 240-250.
T. Jankowski, Fractional differential equations with deviating arguments, Dyn. Syst. Appl. 17 (3-4) (2008), 677684.
T. Jankowski, Existence results to delay fractional differential equations with nonlinear boundary conditions, Appl. Math. Comput. 219 (2013), 9155-9164.
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier, Amsterdam, (2006).
G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Pub. Co, Boston, 1985.
V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal. 69 (2008), 3337-3343.
V. Lakshmikanthan and A. S. Vatsala,General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Lett. 21 (2008), 828-834.
L. Lin, X. Liu and H. Fang, Method of upper and lower solutions for fractional differential equations, Electron. J. Diff. Eqs. 100 (2012), 1-13.
F. A. McRae, Monotone iterative technique and existence results for fractional differential equations, Nonlinear Anal. 71 (2009), 6093-6096.
J. A. Nanware and D. B. Dhaigude, Existence and Uniqueness of solution of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions, Int. J. Nonlinear Sci. 14 (2012), 410-415.
J. A. Nanware and D. B. Dhaigude, and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl. 7 (2014),
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering,
Academic Press, New York (1999).
T. Wang and F. Xie, Existence and uniqueness of fractional differential equations with integral boundary conditions, J. Nonlinear Sci. Appl. 2 (2008), 206-212.
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