An investigation of fractional Bagley-Torvik equation

Abstract

In this paper the authors prove the existence as well as approximations of the solutions for the Bagley-Torvik equation admitting only the existence of a lower (coupled lower and upper) solution. Our results rely on an appropriate fixed point theorem in partially ordered normed linear spaces. Illustrative examples are included to demonstrate the validity and applicability of our technique.

Keywords

• bagley-torvik equation
• fractional calculus
• partially fixed point
• mixed monotone operator
• existence
• uniqueness
• approximation
• 26a33
• 34a08
• 34a12