Fractional Operators in $p$-adic Variable Exponent Lebesgue Spaces and Application to $p$-adic Derivative

Abstract

In this paper, we prove the boundedness of the fractional maximal and the fractional integral operator in the p -adic variable exponent Lebesgue spaces. As an application, we show the existence and uniqueness of the solution for a nonhomogeneous Cauchy problem in the p -adic variable exponent Lebesgue spaces.