SavedAdd your journal

Journals / Konuralp Journal of Mathematics / 2021 / Cilt: 9 - Sayı: 1

Solvability of Fractional Boundary Value Problems for a Combined Caputo Derivative

Şuayip TOPRAKSEVEN
Pages
119–126
Publication Date
2021-04-28
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Various examples are given to show the applications of the results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper deals with a class of boundary value problems of the combined Caputo fractional differential equations.
📊
Key Findings & Data:The main feature of the combined Caputo fractional derivative is that it holds both left and right nonlocal memory effects.
💡
Conclusion & Impact:Various examples are given to show the applications of the results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Combined Caputo derivative · Existence · Fixed point

Abstract

This paper deals with a class of boundary value problems of the combined Caputo fractional differential equations. The main feature of the combined Caputo fractional derivative is that it holds both left and right nonlocal memory effects. By using the fractional Gronwall-type inequalities and some fixed point theorems, we established some necessary conditions for the existence of solutions. Various examples are given to show the applications of the results.

🔖

Cite This Article

TOPRAKSEVEN, Ş. (2021). Solvability of Fractional Boundary Value Problems for a Combined Caputo Derivative. Konuralp Journal of Mathematics, Cilt: 9 - Sayı: 1, 119–126. https://ajindex.com/articles/786405

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. R. Agarwal, D, O’Regan and S. Stanek, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations.J. Math. Anal. Appl., 371 (2010), 57–68
  2. A. Babakhani and V. Gejji, Existence of positive solutions of nonlinear fractional differential equations.J. Math. Anal.Appl. 278, (2003), 434-442
  3. C. Celik and M. Duman, Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative. J. Comput. Phys. 231 (2012) 1743–1750
  4. F. Chen, A. Chen and X. Wu, Anti-periodic boundary value problems with Riesz-Caputo derivative. Adv. Difference Equ. 2019 (2019), 119
  5. Y. Cui, Uniqueness of solution for boundary value problems for fractional differential equations. Appl. Math. Lett. 51 (2016), 48–54
  6. M.Darwish and S. Ntouyas, On initial and boundary value problems for fractional order mixed type functional differential inclusion. Comput. Math. Appl. 59 (2010), 1253–1265
  7. R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini and P. Paradisi, Discrete random walk models for space–time fractional diffusion. Chem. Phys. 284 (2012), 521–541
  8. C. Gu and G. Wu, Positive solutions of fractional differential equations with the Riesz space derivative. Appl. Math. Lett. 95 (2019), 59–64
  9. L. Guo, L. Liu and W. Ye, Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions. Comput. Math. Appl. 59(8) (2010), 2601–2609
  10. A. Kilbas, H.H. Srivastava and J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204.North–Holland mathematics studies,Elsevier, Amsterdam, 2006
  11. M. Klimek, Stationarity-conservation laws for fractional differential equations with variable coefficients. J. Phys. A 35(31) (2002), 6675- 6693
  12. G. Li and H. Liu, Stability analysis and synchronization for a class of fractional-order neural networks, Entropy, 55 (18) (2016), p. 13
  13. K. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations. John Wiley, NY,1993
  14. G. NGereekata, A Cauchy problem for for some fractional abstract differential equations with fractional order with nonlocal conditions. Nonlinear Anal. 70 (2009), 1873–1876
  15. T. Odzijewicz, A.B. Malinowska and D.F.M. Torres, A generalized fractional calculus of variations Control Cybernet., 2 (42) (2013), pp. 443-458
  16. C. Pinto and A.R.M. Carvalho, New findings on the dynamics of HIV and TB coinfection mode