Korean J. Math.  Vol 23, No 1 (2015)  pp.205-230
DOI: https://doi.org/10.11568/kjm.2015.23.1.205

Existence of solutions of a class of impulsive periodic type BVPs for singular fractional differential systems

Yuji Liu

Abstract


A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities $p(t)f(t,x,y)$ and $q(t)g(t,x,y)$ in fractional differential equations to be singular at $t=0,1$ and be involved a sup-multiplicative-like function. So both $f$ and $g$ may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

Keywords


singular fractional differential system, impulsive boundary value problems, fixed point theorem

Subject classification

92D25, 34A37, 34K15

Sponsor(s)

This work was supported by the National Natural Science Foundation of China (No: 11401111), the Natural Science Foundation of Guangdong province (No:S2011010001900) and the Foundation for High-level talents in Guangdong Higher Education Project.

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