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THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON FUNCTIONS
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This paper mainly discusses the influence of the Weyl fractional integrals on continuous functions and proves that the Weyl fractional integrals can retain good properties of many functions. For example, a bounded variation function is still a bounded variation function after the Weyl fractional integral. Continuous functions that satisfy the Holder condition after the Weyl fractional integral still satisfy the Holder condition, furthermore, there is a linear relationship between the order of the Holder conditions of the two functions. At the end of this paper, the classical Weierstrass function is used as an example to prove the above conclusion.
Title: THE EFFECT OF THE WEYL FRACTIONAL INTEGRAL ON FUNCTIONS
Description:
This paper mainly discusses the influence of the Weyl fractional integrals on continuous functions and proves that the Weyl fractional integrals can retain good properties of many functions.
For example, a bounded variation function is still a bounded variation function after the Weyl fractional integral.
Continuous functions that satisfy the Holder condition after the Weyl fractional integral still satisfy the Holder condition, furthermore, there is a linear relationship between the order of the Holder conditions of the two functions.
At the end of this paper, the classical Weierstrass function is used as an example to prove the above conclusion.
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