Abstract
In this article, a class of integral boundary value problems of fractional delayed differential equations is discussed. Based on the Guo–Krasnoselskii theorem, some existence results on the positive solutions are derived. Two simple examples are given to show the validity of the conditions of our main theorems.
Highlights
Differential equation models have been widely used in control system, aerodynamics, fluid flows and many other branches of engineering [1,2,3,4,5,6,7,8,9]
There are many articles devoted to the existence and multiplicity of positive solutions for the fractional boundary value problems, the approaches mainly include Leray–Schauder degree theory [13, 14], the monotone iterative method [15, 16], the Leggett–Williams theorem [17, 18], the fixed point theorem on cones [17,18,19]
In [28], Cabada and Wang considered a class of nonlinear fractional differential equations with integral boundary value conditions:
Summary
Differential equation models have been widely used in control system, aerodynamics, fluid flows and many other branches of engineering [1,2,3,4,5,6,7,8,9]. In [12], the authors study a class of Riemann–Liouville fractional derivative equations and present sufficient condition on the unique positive solution by employing a u0-positive operator. There are many articles devoted to the existence and multiplicity of positive solutions for the fractional boundary value problems, the approaches mainly include Leray–Schauder degree theory [13, 14], the monotone iterative method [15, 16], the Leggett–Williams theorem [17, 18], the fixed point theorem on cones [17,18,19].
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