Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30998
Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions

Authors: Chuanyun Gu


By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: positive solution, fixed point theorem, Fractional differential equation, existence and uniqueness, generalized concave and convex operator, integral boundary conditions

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 666


[1] Samko S G, Kilbas A A, Marichev O I.; Fractional integral and derivatives: theory and applications, Switzerland: Gordon and Breach, 1993.
[2] Podlubny I.; Fractional differential equations, mathematics in science and engineering, New York: Academic Press, 1999.
[3] Zhao Y, Sun S, Han Z.; The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations, Commun Nonlinear Sci Numer Simulat, 2011, 16:2086-2097.
[4] T. Jankowski.; Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions, Nonlinear Anal. 2010, 73: 1289-1299.
[5] Yuan, CJ.; Two positive solutions for -type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations, Commun. Nonlinear Sci. Numer. Simul. 2012, 17: 930-942.
[6] Yongping Sun, Yan Sun.; Positive solutions and monotone iterative sequences for a fractional differential equation with integral boundary conditions, Advances in Difference Equations 2014, 2014:29.
[7] Chengbo zhai, Wenxia Wang, Lingling Zhang.; Generalizations for a class of Concave and Convex Operators, ACTA MATHEMATICA SINICA,Chinese Series,2008,5l(3):529-540.