Application of Integration by Parts for Fractional Calculus in Solving Two Types of Fractional Definite Integrals

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