skip to main content

CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS

*Khairunnisa Fadhilla Ramdhania scopus  -  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

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:

  1. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. Canada: John Wiley & Sons, Inc., 1993
  2. R. M. Yusron and R. R. Wijayanti, Matematika Teknik 2, 1st ed. Malang: Media Nusa Creative, 2020
  3. J. M. Kimeu, ‘Fractional Calculus: Definitions and Applications’, 2009. [Online]. Available: http://digitalcommons.wku.edu/theseshttp://digitalcommons.wku.edu/theses/115
  4. 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/
  5. 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
  6. 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
  7. J. T. Machado, V. Kiryakova, and F. Mainardi, ‘Recent History of Fractional Calculus’, Commun Nonlinear Sci Numer Simul, vol. 16, no. 3, 2011
  8. 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
  9. L. Adam, ‘Fractional Calculus: History, Definitions, and Applications for the Engineer’, University of Notre Dame, 2004
  10. D. Varberg, E. J. Purcell, and S. E. Rigdon, Kalkulus. Jakarta: Erlangga, 2004
  11. H. Nanang et al., KALKULUS. [Online]. Available: www.getpress.co.id, 2023
  12. T. M. Apostol, Mathematical Analysis, 2nd ed. California: Addison Wesley, 1982
  13. J. B. Fraleigh, A First Course in Abstract Algebra. America: Addison Wesley, 1994
  14. A. Arifin, Aljabar I. Bandung: Penerbit ITB, 2000
  15. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory And Applications of Fractional Differential Equations, 1st ed. Amsterdam: Elsevier, 2006
  16. R. Munir, Matematika Diskrit, 6th ed. Bandung: Informatika Bandung, 2016

Last update:

No citation recorded.

Last update:

No citation recorded.