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Dergiler / Konuralp Journal of Mathematics / 2017 / Volume: 5 Issue: 2

A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL

Abdullah Akkurt0000-0001-5644-1276
Merve Esra Yıldırım
Hüseyin Yıldırım
Sayfa
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Yayın Tarihi
2017-10-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We give some examples.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel.
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Temel Bulgular & Veri:By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem.
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Sonuç & Katkı:We give some examples.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fractional Calculus · Fractional derivative · Conformable Fractional Integral

Abstract

In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem. We give some examples.

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Bu Makaleye Atıf Yap

Akkurt, A., Yıldırım, M. E., Yıldırım, H. (2017). A NEW GENERALIZED FRACTIONAL DERIVATIVE AND INTEGRAL. Konuralp Journal of Mathematics, Volume: 5 Issue: 2. https://ajindex.com/articles/1521836

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Kaynakça (16)

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  2. R. Almeida, M. Guzowska and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, arXiv preprint arXiv:1612.00214.
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  4. U. Katumgapola, A new fractional derivative with classical properties, preprint.
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  12. J. Vanterler da C. Sousa, E. Capelas de Oliveira, A new truncated M-fractional derivative unifying some fractional derivatives with classical properties, arXiv:1704.08187.
  13. J. Vanterler da C. Sousa, E. Capelas de Oliveira, M -fractional derivative with classical properties, arXiv:1704.08186.
  14. M. Z. Sarikaya, H. Budak and F.Usta, On generalized the conformable fractional calculus, RGMIA Research Report Collection, 19 (2016), Article 121, 7 pp.
  15. A. Akkurt, M.E. Yıldırım and H. Yıldırım, On Some Integral Inequalities for Conformable Fractional Integrals, Asian Journal of Mathematics and Computer Research, 15(3): 205-212, 2017.
  16. J. Vanterler da C. Sousa, E. Capelas de Oliveira, M -fractional derivative with classical properties, arXiv:1704.08186.