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.
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