TY - JOUR
T1 - On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems
AU - Abdulla, Arwa Ba
AU - Al-Refai, Mohammed
AU - Al-Rawashdeh, Ahmed
N1 - Publisher Copyright:
© 2015 The Authors.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this paper, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1. <. δ. <. 2. We first transform the problem to an equivalent system of equations, including integer and fractional derivatives. We then implement the method of upper and lower solutions to establish existence and uniqueness results to the resulting system. At the end, some examples are presented to illustrate the validity of our results.
AB - In this paper, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1. <. δ. <. 2. We first transform the problem to an equivalent system of equations, including integer and fractional derivatives. We then implement the method of upper and lower solutions to establish existence and uniqueness results to the resulting system. At the end, some examples are presented to illustrate the validity of our results.
KW - Boundary value problems
KW - Caputo fractional derivative
KW - Fractional differential equations
KW - Lower and upper solutions
KW - Maximum principle
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U2 - 10.1016/j.jksus.2015.05.001
DO - 10.1016/j.jksus.2015.05.001
M3 - Article
AN - SCOPUS:84955206761
SN - 1018-3647
VL - 28
SP - 103
EP - 110
JO - Journal of King Saud University - Science
JF - Journal of King Saud University - Science
IS - 1
ER -