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Dergiler / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 16 Sayı: 2

On Existence and Uniqueness of Some Fractional Order Integro-Differential Equation

Lale Cona(Gümüşhane Üniversitesi Mühendislik Fakültesi Matematik Bölümü)0000-0002-2744-1960
Esmahan Bal(GUMUSHANE UNIVERSITY, INSTITUTE OF SCIENCE, MATH)0000-0002-0135-9176
Sayfa
297–310
Yayın Tarihi
2023-08-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, the results found is supported by examples.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, a sufficient condition for the existence and uniqueness of some fractional order Integral-Differential equations is obtained.
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Temel Bulgular & Veri:Therefore, the fixed point method is used to solve the differential equation problem involving nonlinear degree integrals.
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Sonuç & Katkı:In addition, the results found is supported by examples.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Initial value problem · Fractional order Integro-Differential equation · Riemann-Liouville derivative

Abstract

In this study, a sufficient condition for the existence and uniqueness of some fractional order Integral-Differential equations is obtained. Therefore, the fixed point method is used to solve the differential equation problem involving nonlinear degree integrals. In addition, the results found is supported by examples.

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Bu Makaleye Atıf Yap

Cona, L., Bal, E. (2023). On Existence and Uniqueness of Some Fractional Order Integro-Differential Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 16 Sayı: 2, 297–310. https://doi.org/10.18185/erzifbed.1220243

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Kaynakça (20)

  1. Petras, I. (2011). Fractional-order nonlinear systems modeling, Analysis and Simulation, Springer. New York.
  2. Ashyralyev A. (2009). A note on fractional derivatives and fractional powers of operators. JMAA. 357; 232-236.
  3. Ashyralyev A. (2013). Well-posedness of fractional parabolic equations, Boundary Value Problems. 31; 1-18.
  4. Ashyralyev A. and Cakir, Z. (2013). FDM for fractional parabolic equations with the Neumann condition. Advances in Difference Equations, 2013(120), doi:10.1186/1687-1847-2013-120.
  5. Ashyralyev A., Emirov N. and Cakir Z. (2014). Well-posedness of fractional parabolic differential and difference equations with Dirchlet-Neumann condition, Electronic Journal of Differential Equations. 2014 (97); 1-17.
  6. Podlubny, I. (1999). Fractional differential equations. Mathematics in science and engineering, vol 198. Academic Press. San Diego.
  7. Samko S.G., Kilbas A.A., Marichev O.I. (1993). Fractional Integrals and Derivatives. Gordon & Breach. Yverdon.
  8. Baleanu D, Garra, R, Petras, I. (2013). A fractional variational approach to the fractional Basset-Type equation, Reports on Mathematical Physics. 72 (1); 57-64.
  9. Diethelm, K. and Ford, J.N. (2002). Analysis of fractional differential equations. JMAA. 265; 229-248.
  10. Cona, L. (2017). Fixed point approach to Basset problem. New Trends in Mathematical Sciences. 5(3); 175-181.
  11. Cona, L. (2017). Fixed point approach to Bagley Torvik problem. Communication in Mathematical Modeling and Applications. 2(3), 50--57.
  12. Bai, Z., Sun, S. and Chen, Y.Q. (2014).The existence and uniqueness of a class of fractional differential equations. Abstract and Applied Analysis, Hindawi Publishing Corporation.2014;1-6.
  13. Ashyralyev A. (2013). Computational mathematics textbook, Shymkent.
  14. Kimeu, Joseph M. (2009). Fractional calculus: Definitions and applications. Masters Theses & Specialist Projects. Paper 115. (https://digitalcommons.wku.edu/theses/115)
  15. Kreyszig, E. (1978). Introductory functional analysis with applications, John Willey & Sons, New York.
  16. Caputo, M., Fabrizo, M. (2015). A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl., 1(2), 73-85.
  17. Atangana, A. Baleanu, D. (2016). New fractional derivative with non-local and non-singular kernel, Therm. Sci., 20(2), 757-763.
  18. Yang, X.J., Sirivasta, H.M., Machado, J.A.T. (2016). A new fractional derivatives without singular kernel: application to the modelling of the steady heat flow, Therm. Sci., 20, 753-756.
  19. Vanterler da Sausa, J., Capelas de Oliveira C., E. (2017). A new fractional derivative of variable order with non-singular order and fractional differential equations, arXiv: 1712.06506v1.
  20. Vanterler da Sausa, J., Capelas de Oliveira C., E. (2020). On the Ψ-Hilfer fractional derivative, Commun Nonlinear Sci. Numer, Simul. 60, 72-91.