Abstract
In this paper, we discuss the existence and multiplicity of positive solutions for a system of fractional differential equations with boundary condition and advanced arguments. The existence result is proved via Leray–Schauder’s fixed point theorem type in a vector Banach space. Further, by using a new fixed point theorem in order Banach space, we study the multiplicity of positive solutions. Finally, some examples are given to illustrate our results.
Highlights
Fractional calculus and differential equations have proved to be important tools modeling many real world phenomena like chemistry and physics [11, 22, 23, 25])
There have been some papers dealing with the existence and multiplicity of solution of nonlinear initial fractional differential equation by the use of techniques of nonlinear analysis, see [2,3,4,5,6,7, 9, 33, 35, 38]
Chai obtained in [10] the existence of at least one nonnegative solution and two positive solutions by using fixed point theorem on cone for the following problem:
Summary
Fractional calculus and differential equations have proved to be important tools modeling many real world phenomena like chemistry and physics [11, 22, 23, 25]). There have been some papers dealing with the existence and multiplicity of solution (or positive solution) of nonlinear initial fractional differential equation by the use of techniques of nonlinear analysis, see [2,3,4,5,6,7, 9, 33, 35, 38]. Chai obtained in [10] the existence of at least one nonnegative solution and two positive solutions by using fixed point theorem on cone for the following problem:. Su et al [31] studied the existence of one and two positive solutions by using the fixed point index theory of the following boundary values problems:.
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