Abstract: In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we solve two types of fractional definite integrals of fractional trigonometric functions. The exact solutions of these two types of fractional definite integrals can be obtained by using integration by parts for fractional calculus. Moreover, we give some examples to illustrate our results. On the other hand, our results are generalizations of the classical calculus results. Keywords: Jumarie type of R-L fractional calculus, new multiplication, fractional analytic functions, fractional definite integrals, fractional trigonometric functions, integration by parts for fractional calculus. Title: Application of Integration by Parts for Fractional Calculus in Solving Two Types of Fractional Definite Integrals Author: Chii-Huei Yu International Journal of Novel Research in Electrical and Mechanical Engineering ISSN 2394-9678 Vol. 10, Issue 1, September 2022 - August 2023 Page No: 79-84 Novelty Journals Website: www.noveltyjournals.com Published Date: 13-June-2023 DOI: https://doi.org/10.5281/zenodo.8033205 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/Application%20of%20Integration-13062023-2.pdf

International Journal of Novel Research in Electrical and Mechanical Engineering, ISSN 2394-9678, Novelty Journals, Website: www.noveltyjournals.com