OPIAL-TYPE INEQUALITY ABOUT CONFORMABLE FRACTIONAL INTEGRALS AND THE APPLICATION

Yongfang Qi, Guoping Li and Xiaoyuan Wang
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Yongfang Qi: Department of Mathematics, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China
Guoping Li: ��Scientific Research Planning Division, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China
Xiaoyuan Wang: Department of Mathematics, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-11

Abstract: In this paper, we define partial conformable fractional derivative (PCFD) which is based on the fractional derivative definition proposed by Abdeljawad. At the same time, we present some simple properties about the definition, the properties are useful for us when we carry out further research. In addition, taking advantage of Hölder’s inequality, we establish Opial-type inequalities for the partial conformable fractional (PCF) integral. As an application, the uniqueness of the partial system with initial value is proved.

Keywords: Opial-Type Inequality; Conformable; Hölder’s Inequality; Uniqueness (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500584

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