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All Journal Journal of Fundamental Mathematics and Applications (JFMA)
Pratama, Aldira Ryan
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Decision Sciences, Operations Research & Management

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CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS Ramdhania, Khairunnisa Fadhilla; Sari, Rafika; Khalida, Rakhmi; Pratama, Aldira Ryan; Lestari, Nur’aini Puji
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.19256

Abstract

This paper discusses the theory of derivatives and integrals in the form of fractions with a particular order initiated by Lioville. Specifically, regarding the correlation between fractional derivatives and integrals, by examining definitions, determining the kernel function, and applying them to several examples, so a general formula will be obtained regarding the relationship between the two. This formula is the product of the fractional derivative of an order of a polynomial function of m-degree which is equal to the (n+1) th derivative of the related order fractional integral of a polynomial function of -degree that the truth is proved by using Mathematical Induction.
Co-Authors Khalida, Rakhmi Lestari, Nur’aini Puji Rafika Sari Ramdhania, Khairunnisa Fadhilla