Abstract
We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.
Highlights
Fractional differential equations describe many phenomena in various fields of engineering and scientific disciplines such as physics, biophysics, chemistry, biology, economics, control theory, signal and image processing, aerodynamics, viscoelasticity, electromagnetics, and so on
We consider the system of nonlinear ordinary fractional differential equations (S)
We mentioned the paper [21], where we investigated the existence and multiplicity of positive solutions for the system D0α+u (t ) + f (t, v (t )) = 0, t ∈ (0,1), D0β+v (t ) + g (t,u (t )) = 0, t ∈ (0,1), with the integral boundary conditions (BC) with a=0 b=0 0 by using some theorems from the fixed point index theory and the
Summary
Fractional differential equations describe many phenomena in various fields of engineering and scientific disciplines such as physics, biophysics, chemistry, biology (such as blood flow phenomena), economics, control theory, signal and image processing, aerodynamics, viscoelasticity, electromagnetics, and so on (see [1]-[6]). Some systems of fractional equations with parameters subject to coupled integral boundary conditions were studied in [20] by using the Guo-Krasnosel’skii fixed point theorem. We mentioned the paper [21], where we investigated the existence and multiplicity of positive solutions for the system D0α+u (t ) + f (t, v (t )) = 0, t ∈ (0,1) , D0β+v (t ) + g (t,u (t )) = 0, t ∈ (0,1) , with the integral boundary conditions (BC) with a=0 b=0 0 by using some theorems from the fixed point index theory and the. If the operator A : Y → Y is completely continuous, A has at least one fixed point
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