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Article

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

Department of Business Administration, Mardin Artuklu University, 47200 Mardin, Turkey
Fractal Fract. 2021, 5(1), 7; https://doi.org/10.3390/fractalfract5010007
Received: 5 November 2020 / Revised: 4 January 2021 / Accepted: 5 January 2021 / Published: 8 January 2021
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-α integral operator Ma,δc to the norm of the centered fractional maximal diamond-α integral operator Mac 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. View Full-Text
Keywords: time scales; variable exponent; fractional integral; maximal operator time scales; variable exponent; fractional integral; maximal operator
MDPI and ACS Style

Akın, L. A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces. Fractal Fract. 2021, 5, 7. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010007

AMA Style

Akın L. A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces. Fractal and Fractional. 2021; 5(1):7. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010007

Chicago/Turabian Style

Akın, Lütfi. 2021. "A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces" Fractal and Fractional 5, no. 1: 7. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010007

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