Abstract: Fractional calculus is widely used in many scientific fields. This paper uses a new method to study fractional integral calculus. Based on the Jumarie type of modified Riemann-Liouville (R-L) fractional derivative, we make use of a new multiplication and some techniques include integration by parts for fractional calculus to solve some problems of fractional integral. The modified Jumarie’s R-L fractional derivative is closely related to classical calculus, which can make the fractional derivative of constant function to zero. Seven kinds of special fractional integral problems are provided, and the results we obtained are the generalizations of classical integral problems. Furthermore, Mittag-Leffler function plays an important role in this study, which is similar to the exponential function in traditional calculus. On the other hand, several examples are given to illustrate our results.
Keywords: Jumarie type of modified R-L fractional derivative, New multiplication, Integration by parts for fractional calculus, Problems of fractional integral, Mittag-Leffler function.
Title: A New Approach to Study Fractional Integral Problems
Author: Chii-Huei Yu
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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