CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS - Ramdhania, Khairunnisa Fadhilla; Sari, Rafika; Khalida, Rakhmi; Pratama, Aldira Ryan; Lestari, Nur’aini Puji (Diponegoro University, 2024)
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.