Existence of Positive Solutions of Boundary Value Problem For FractionalOrder Differential Equation
JOURNAL OF EDUCATION AND SCIENCE,
2020, Volume 29, Issue 2, Pages 149-157
AbstractRecently boundary value problems for differential equations of non-integral order have studied in many papers ( see [1,2] ).
Zaho etal [ 1 ] studied the following boundary value problem of fractional differential equations.
Where denotes the Rimann-Liouville fractional derivative equation of order . By using the lower and upper solution method and fixed point theorem.
Liang and Zhang  studied the non-linear fractional differential boundary value problem
Where is a real number . is the Rimann-Liouville fractional differential operator of order . By means of fixed point theorems , they obtained results on the existence of positive solutions for boundary value problem of fractional differential equations.
In this paper , we deal with some existence of positive solution of the following non-linear fractional differential equation.
Where is a real number. denotes Rimann-Liouville fractional derivative of order .
Our work based on Banach contraction mapping and Krasnoel'skii fixed point theorems to investigate the existence of positive solution.
Finally , we suggest studing the existence solutions for the following Integrodifferential equation with boundary value conditions
Where H is a nonlinear integral operator given as
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