A nonstandard Volterra integral equation on time scales

Abstract

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

Keywords

• volterra integral equations
• time scales
• bounded solution
• continuous dependence
• 45d05
• 45g10
• 34n05