Positive Solutions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1,1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

Abstract

We study the positive solutions of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1,1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.