KaydedilenlerDerginizi ekleyin

Dergiler / Bilgisayar Bilimleri / 2021 / Cilt: 6 - Sayı: 2

Fractional Order Integration: A New Perspective based on Karcı’s Fractional Order Derivative

Ali KARCİ
Sayfa
102–105
Yayın Tarihi
2021-06-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, a new definition for fractional order integral was emphasized based on the definition for fractional order derivative made by Karcı.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:There are many methods/definitions for fractional order derivatives, and naturally, there are many definitions for fractional order integrals based on these definitions.
📊
Temel Bulgular & Veri:There are many methods/definitions for fractional order derivatives, and naturally, there are many definitions for fractional order integrals based on these definitions.
💡
Sonuç & Katkı:In this paper, a new definition for fractional order integral was emphasized based on the definition for fractional order derivative made by Karcı.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fractional Calculus · Integration · Fractional Order Derivatives

Özet

There are many methods/definitions for fractional order derivatives, and naturally, there are many definitions for fractional order integrals based on these definitions. In this paper, a new definition for fractional order integral was emphasized based on the definition for fractional order derivative made by Karcı.

Abstract

There are many methods/definitions for fractional order derivatives, and naturally, there are many definitions for fractional order integrals based on these definitions. In this paper, a new definition for fractional order integral was emphasized based on the definition for fractional order derivative made by Karcı.

🔖

Bu Makaleye Atıf Yap

KARCİ, A. (2021). Fractional Order Integration: A New Perspective based on Karcı’s Fractional Order Derivative. Bilgisayar Bilimleri, Cilt: 6 - Sayı: 2, 102–105. https://ajindex.com/articles/743198

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. Baron, M.E.,”The Origin of the Infinitesimal Calculus”, New York, 1969.
  2. Bataineh, A.S., Alomari, A.K., Noorani, M.S.M., Hashim, I., Nazar, R.,”Series Solutions of Systems of Nonlinear Fractional Differential Equations”, Acta Applied Mathematics, 105:189-198,2009.
  3. Das, S.,”Functional Fractional Calculus”, Springer-Verlag Berlin Heidelberg, 2011.
  4. Diethelm, K., Ford, N.J., Freed, A.D., Luchko, Y.,”Algorithms fort he Fractional Calculus: A Selection of Numerical Methdos, Computer Methods in Applied Mechanics and Engineering”, 194:743-773,2005.
  5. Goldenbaum, U., Jesseph, D.,”Infinitesimal Differences: Controversies between Leibniz and his Contemporaries”, New York, 2008.
  6. He, J.-H., Elagan,S.K., Li,Z.B., “Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus”, Physics Letters A, 376:257-259, 2012.
  7. Karcı, A., “Kesirli Türev için Yapılan Tanımlamaların Eksiklikleri ve Yeni Yaklaşım”, TOK-2013 Turkish Automatic Control National Meeting and Exhibition, Malatya, Turkey, 2013a.
  8. Karcı, A.,”A New Approach for Fractional Order Derivative and Its Applications”, Universal Journal of Engineering Sciences, 1:110-117, 2013b.
  9. Karcı, A., “Properties of Fractional Order Derivatives for Groups of Relations/Functions”, Universal Journal of Engineering Sciences, vol: 3, pp: 39-45, 2015a.
  10. Karcı, A.,”The Linear, Nonlinear and Partial Differential Equations are not Fractional Order Differential Equations”, Universal Journal of Engineering Sciences, vol: 3, pp: 46-51, 2015b.
  11. Karcı, A.,“Generalized Fractional Order Derivatives for Products and Quotients”, Science Innovation, vol:3, pp:58-62, 2015c.
  12. Karcı, A.,“Chain Rule for Fractional Order Derivatives”, Science Innovation, vol:3, 63-67, 2015d. Karcı,A., “The Properties of New Approach of Fractional Order Derivative”, Journal of the Faculty of Engineering and Architecture of Gazi University, Vol.30, pp: 487-501, 2015e.
  13. Karcı, A.,“Fractional order entropy New perspectives”, Optik - International Journal for Light and Electron Optics, Vol:127, no:20, pp:9172-9177, 2016.
  14. Karcı, A.,“Malatya Functions: Symmetric Functions Obtained by Applying Fractional Order Derivative to Karcı Entropy”, Anatolian Science-Journal of Computer Sciences, Vol:2, Issue: 2, pp:1-8, 2017.
  15. Kilbas, A.A., Srivastava, H.M., Trujillo,J.J.”Theory and Applications of Fractional Differential Equations”, Elsevier, 2006. L'Hôpital, G. 1696. Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes ("Infinitesi