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

Yuji Liu
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2015.03|한국수학논문집 (Korean Journal of Mathematics)|제23권 제1호|pp. 205-230|DOI http://dx.doi.org/10.11568/kjm.2015.23.1.205

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키워드

fixed point theoremsingular fractional differential systemimpulsive boundary value problems
주제분류수학

초록

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.

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.

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