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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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

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