Uniqueness and existence of positive solutions for the fractional integro-differential equation

In this paper, we study the uniqueness and existence of positive solutions for the fractional integro-differential equation with the integral boundary value problem. By means of the Banach contraction principle and the Krasnoselskii fixed point theorem, the sufficient conditions on the uniqueness and existence of positive solutions are investigated. An example is given to illustrate the main results.

[1]  Ingo Schäfer,et al.  Fractional Calculus via Functional Calculus: Theory and Applications , 2002 .

[2]  Lishan Liu,et al.  Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions , 2016 .

[3]  Ying Wang,et al.  Positive solutions for higher-order singular fractional differential system with coupled integral boundary conditions , 2016 .

[4]  Yonghong Wu,et al.  Positive solutions for singular nonlinear fractional differential equation with integral boundary conditions , 2015 .

[5]  Lishan Liu,et al.  Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters , 2014 .

[6]  Teodor M. Atanackovic,et al.  On a class of differential equations with left and right fractional derivatives , 2007 .

[7]  E. Zeidler,et al.  Fixed-point theorems , 1986 .

[8]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[9]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[10]  Lishan Liu,et al.  The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems , 2016 .

[11]  KEVIN G. TEBEEST.  Classroom Note: Numerical and Analytical Solutions of Volterra's Population Model , 1997, SIAM Rev..

[12]  Yonghong Wu,et al.  Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions , 2016 .

[13]  Hang Xu,et al.  Analytical approximations for a population growth model with fractional order , 2009 .

[14]  Lishan Liu,et al.  Iterative positive solutions for singular nonlinear fractional differential equation with integral boundary conditions , 2016 .

[15]  Xinguang Zhang,et al.  Spectral Analysis for a Singular Differential System with Integral Boundary Conditions , 2016 .

[16]  Lishan Liu,et al.  Existence of solutions for a sequential fractional differential system with coupled boundary conditions , 2016 .

[17]  Ying Wang,et al.  Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection , 2015, Appl. Math. Comput..

[18]  Lingju Kong,et al.  Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives , 2013 .

[19]  Zhimin He,et al.  Existence of solutions for nonlinear high-order fractional boundary value problem with integral boundary condition , 2014 .

[20]  Zhanbing Bai,et al.  Existence of positive solution for singular fractional differential equation , 2009, Appl. Math. Comput..

[21]  I. Podlubny.  Fractional differential equations , 1998 .

[22]  R. Feynman,et al.  RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING , 2003 .

[23]  Yonghong Wu,et al.  The uniqueness of positive solution for a fractional order model of turbulent flow in a porous medium , 2014, Appl. Math. Lett..

[24]  Lishan Liu,et al.  Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions , 2016 .

[25]  A. Cabada,et al.  Positive solutions of nonlinear fractional differential equations with integral boundary value conditions , 2012 .

[26]  F. M. Scudo,et al.  Vito Volterra and theoretical ecology. , 1971, Theoretical population biology.

[27]  Yonghong Wu,et al.  Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions , 2016 .