Solving Some Type of Improper Fractional Integral Using Differentiation under Fractional Integral Sign and Integration by Parts for Fractional Calculus

Abstract: In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study some type of improper fractional integral. We can obtain the exact solution of this improper fractional integral by using differentiation under fractional integral sign and integration by parts for fractional calculus. In fact, our result is a generalization of classical calculus result. Keywords: Jumarie’s modified R-L fractional calculus, new multiplication, fractional analytic functions, improper fractional integral, differentiation under fractional integral sign, integration by parts for fractional calculus. Title: Solving Some Type of Improper Fractional Integral Using Differentiation under Fractional Integral Sign and Integration by Parts for Fractional Calculus Author: Chii-Huei Yu, Kuang-Wu Yang International Journal of Engineering Research and Reviews ISSN 2348-697X (Online) Vol. 12, Issue 4, October 2024 - December 2024 Page No: 34-38 Research Publish Journals Website: www.researchpublish.com Published Date: 16-October-2024 DOI: https://doi.org/10.5281/zenodo.13939320 Paper Download Link (Source) https://www.researchpublish.com/papers/solving-some-type-of-improper-fractional-integral-using-differentiation-under-fractional-integral-sign-and-integration-by-parts-for-fractional-calculus