Green's Functions of Some Non‐Integer‐Order Initial and Boundary Value Problems

Source abstract

ABSTRACT In this paper we introduce Green's functions of some scalar initial and boundary‐value problems generated by non‐integer‐order symmetric differential equations. In particular, we consider ‐sequential and ‐sequential initial and boundary‐value problems, and using some properties of the Dirac‐delta function we introduce the solutions of these problems. Such problems are constructed by Riemann–Liouville and Caputo type differential operators. Moreover, we share an existence and uniqueness theorem.