CONSTRUCTION OF FUNDAMENTAL THEOREMS  OF FRACTIONAL CALCULUS

Khairunnisa Fadhilla Ramdhania; Rafika Sari; Rakhmi Khalida; Aldira Ryan Pratama; Nur’aini Puji Lestari

doi:10.14710/jfma.v7i1.19256

DOI: https://doi.org/10.14710/jfma.v7i1.19256

CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS

*Khairunnisa Fadhilla Ramdhania

- Universitas Bhayangkara Jakarta Raya, Indonesia

Rafika Sari - Program Studi Informatika, Fakultas Ilmu Komputer, Universitas Bhayangkara Jakarta Raya, Indonesia

Rakhmi Khalida - Program Studi Informatika, Fakultas Ilmu Komputer, Universitas Bhayangkara Jakarta Raya, Indonesia

Aldira Ryan Pratama - Program Studi Informatika, Fakultas Ilmu Komputer, Universitas Bhayangkara Jakarta Raya, Indonesia

Nur’aini Puji Lestari - Program Studi Informatika, Fakultas Ilmu Komputer, Universitas Bhayangkara Jakarta Raya, Indonesia

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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.

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Keywords: fractional derivative; fractional integral; Fundamental Theorem of Calculus

Funding: Universitas Bhayangkara Jakarta Raya

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS

Language : EN

In Vol 7, No 1 (2024)

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