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Existence of a solution for the fractional differential equation with nonlinear boundary conditions. (English) Zbl 1217.34011
Summary: Using the method of upper and lower solutions and its associated monotone iterative, we present an existence theorem for a nonlinear fractional differential equation with nonlinear boundary conditions.
MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
45J05Integro-ordinary differential equations
References:
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[3]Franco, Daniel; Nieo, Juan J.; O’regan, Donal: Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions, Appl. math. Comput. 153, 793-802 (2004) · Zbl 1058.34015 · doi:10.1016/S0096-3003(03)00678-7
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[7]Zhang, Shuqin: Monotone iterative method for initial value problem involving Riemann–Liouville fractional derivatives, Nonlinear anal. 71, 2087-2093 (2009) · Zbl 1172.26307 · doi:10.1016/j.na.2009.01.043
[8]Bhaskar, T. G.; Lakshmikantham, V.; Devi, J. V.: Monotone iterative technique for functional differential equations with retardation and anticipation, Nonlinear anal. 66, 2237-2242 (2007) · Zbl 1121.34065 · doi:10.1016/j.na.2006.03.013
[9]Zhang, Shuqin: The existence of a positive solution for a nonlinear fractional differential equation, J. math. Anal. appl. 252, 804-812 (2000) · Zbl 0972.34004 · doi:10.1006/jmaa.2000.7123
[10]Zhang, Shuqin: Positive solution for some class of nonlinear fractional differential equation, J. math. Anal. appl. 278, No. 1, 136-148 (2003) · Zbl 1026.34008 · doi:10.1016/S0022-247X(02)00583-8