Differentiation of Solutions of Caputo Boundary Value Problems with Respect to Boundary Data

Abstract

Under suitable continuity and uniqueness conditions, solutions of an α order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used applies a standard algorithm to achieve the result and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.

Keywords

• Caputo fractional differential equation
• boundary value problem
• continuous dependence
• variational equation