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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 2

New existence results for positive solutions of boundary value problems for coupled systems of multi-term fractional differential equations

Yuji Liu
Sayfa
391–416
Yayın Tarihi
2022-10-18
DOI
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Numerical examples are given to illustrate the main theorems.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this article, we establish some new existence results on positive solutions of a boundary value problem of coupled systems of nonlinear multi-term fractional differential equations.
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Temel Bulgular & Veri:Our analysis rely on the well known fixed point theorems.
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Sonuç & Katkı:Numerical examples are given to illustrate the main theorems.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Four-point boundary value problem · multi-term fractional differential system · non-Caratheodory function

Abstract

In this article, we establish some new existence results on positive solutions of a boundary value problem of coupled systems of nonlinear multi-term fractional differential equations. Our analysis rely on the well known fixed point theorems. Numerical examples are given to illustrate the main theorems.

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Bu Makaleye Atıf Yap

Liu, Y. (2022). New existence results for positive solutions of boundary value problems for coupled systems of multi-term fractional differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 2, 391–416. https://ajindex.com/articles/530028

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Kaynakça (14)

  1. Ahmad, A. and Nieto, J.J. Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58, 1838- 1843, 2009.
  2. Ahmad, B. and Sivasundaram, S. On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order, Appl. Math. Comput. 217, 480-487, 2010. Avery R.I., and Peterson, A.C. Three Positive Fixed Points of Nonlinear Operators on Ordered Banach Spaces, Comput. Math. Appl. 42, 313-322, 2001.
  3. Basset, A.B. On the descent of a sphere in a vicous liquid, Q. J. Pure Appl. Math. 41, 369-381, 1910.
  4. Bai, C. and Fang, J. The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Appl. Math. Comput. 150, (3), 611-621, 2004.
  5. Caponetto, R., Dongona, G. and Fortuna, L. Fractional Differential Systems, Modeling and control applications, World Scientific Series on Nonlinear Science, Ser. A, 72, World Scientific Publishing Co. Pte. Ltd. 2010.
  6. Duan, J. and Temuer, C. Solution for system of linear fractional differential equations with constant coefficients, Journal of Mathematics, 29, 599-603, 2009.
  7. Gaber, M. and Brikaa, M.G. Existence results for a coupled system of nonlinear fractional differential equation with four-point boundary conditions, ISRN Mathematical Analysis, 2011, Article ID 468346, 14 pages, 2011.
  8. Goodrich, C.S. Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl. 62, 1251-1268, 2011.
  9. Liu, B. Positive solutions of a nonlinear four-point boundary value problems in Banach spaces, J. Math. Anal. Appl. 305, 253-276, 2005.
  10. Liu, L., Zhang, X. and Wu, Y. On existence of positive solutions of a two-point boundary value problem for a nonlinear singular semipositone system, Appl. Math. Comput. 192, 223-232, 2007.
  11. Mainardi, F. Fraction Calculus: Some basic problems in continuum and statistical machanics, In: A. Carpinteri, F. Mainardi (eds.) Fratals and Fractional Calculus in Continuum Machanics, (Springer, Vien, 1997), 291-348.
  12. Miller, K.S. and Ross, B. An Introduction to the Fractional Calculus and Fractional Differential Equation, (Wiley, New York, 1993.)
  13. Mamchuev, M.O. Boundary value problem for a system of fractional partial differential equations, Partial Differential Equations, 44, 1737-1749, 2008.
  14. Rehman, M. and Khan, R. A note on boundaryvalueproblems for a coupled system of fractionaldifferential equations, Comput. Math.