Inhomogeneous conformable abstract Cauchy problem

Abstract

In this paper, we discuss the solution of the inhomogeneous conformable abstract Cauchy problem. The homogeneous problem is also studied. The analysis of conformable fractional calculus and fractional semigroups is also given. Existence, uniqueness and regularity of a mild solution for the conformable abstract Cauchy problem are studied. Applications illustrating our main abstract results are also given.

Keywords

• α-semigroup of operators
• conformable derivative
• inhomogeneous cauchy problem
• 34g10
• 26a33