A New Approach for the Fractional Integral Operator in Time Scales With Variable Exponent Lebesgue Spaces

Abstract

Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond-alpha integral operator M-a,delta(c) to the norm of the centered fractional maximal diamond-alpha integral operator M-a(c) on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales.