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

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Citation Format:

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.

Fulltext View|Download

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

Funding: Universitas Bhayangkara Jakarta Raya

Article Metrics:

Article Info

Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS

Language : EN

In Vol 7, No 1 (2024)

Recent articles

THE L(2,1)-LABELING OF MONGOLIAN TENT, LOBSTER, TRIANGULAR SNAKE, AND KAYAK PADDLE GRAPH THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER OPTIMAL CONTROL OF MATHEMATICAL MODELS IN BIOENERGY SYSTEMS AS EMPOWERMENT OF SUSTAINABLE ENERGY SOURCES More recent articles

K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. Canada: John Wiley & Sons, Inc., 1993
R. M. Yusron and R. R. Wijayanti, Matematika Teknik 2, 1st ed. Malang: Media Nusa Creative, 2020
J. M. Kimeu, ‘Fractional Calculus: Definitions and Applications’, 2009. [Online]. Available: http://digitalcommons.wku.edu/theseshttp://digitalcommons.wku.edu/theses/115
J. A. T. Machado, V. Kiryakova, and F. Mainardi, ‘A Poster about The Old History of Fractional Calculus’, An International Journal for Theory and Aplication, vol. 13, pp. 447–453, 2010, [Online]. Available: http://www.math.bas.bg/
H. V. Dannon, ‘The Fundamental Theorem of the Fractional Calculus, and the Meaning of Fractional Derivatives’, Gauge Institute Journal, vol. 5, no. 1, Feb. 2009
I. Podlubny, A. Chechkin, T. Skovranek, Y. Chen, and B. M. J. Vinagre, ‘Matrix Approach to Discrete Fractional Calculus II: Partial Fractional Differential Equations’, J Comput Phys, vol. 228, pp. 3137–3153, 2009
J. T. Machado, V. Kiryakova, and F. Mainardi, ‘Recent History of Fractional Calculus’, Commun Nonlinear Sci Numer Simul, vol. 16, no. 3, 2011
H. Gunawan, E. Rusyaman, and L. Ambarwati, ‘Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order’, ITB J. Sc, vol. 43A, pp. 209–222, 2011
L. Adam, ‘Fractional Calculus: History, Definitions, and Applications for the Engineer’, University of Notre Dame, 2004
D. Varberg, E. J. Purcell, and S. E. Rigdon, Kalkulus. Jakarta: Erlangga, 2004
H. Nanang et al., KALKULUS. [Online]. Available: www.getpress.co.id, 2023
T. M. Apostol, Mathematical Analysis, 2nd ed. California: Addison Wesley, 1982
J. B. Fraleigh, A First Course in Abstract Algebra. America: Addison Wesley, 1994
A. Arifin, Aljabar I. Bandung: Penerbit ITB, 2000
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory And Applications of Fractional Differential Equations, 1st ed. Amsterdam: Elsevier, 2006
R. Munir, Matematika Diskrit, 6th ed. Bandung: Informatika Bandung, 2016

Last update:

No citation recorded.

Last update:

No citation recorded.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors who publish articles in this journal agree to the following terms:

Authors grant the journal the right of first publication that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.

For more detailed information about the copyright transfer, please refer to this page: COPYRIGHT TRANSFER FORM

CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS

EDITORIAL OFFICE

INDEXED IN: