Journals / Fundamental Journal of Mathematics and Applications / 2022 / Cilt: 5 Sayı: 2

Analysis of a System of Nonlinear Hadamard Type Fractional Boundary Value Problems

Pages
114–126
Publication Date
2022-06-01
DOI
—
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AI Summary & Key Takeaways

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

Finally, to show the applicability of the main result, an illustrative example is also involved.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this work is to analyze the existence of positive solutions for a coupled system of Hadamard type fractional boundary value problems.
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Key Findings & Data:By using the five functional fixed point theorem, the conditions for the existence of positive solutions are derived.
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Conclusion & Impact:Finally, to show the applicability of the main result, an illustrative example is also involved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fixed-point theorem · Hadamard fractional differential systems · Positive solutions

Abstract

The aim of this work is to analyze the existence of positive solutions for a coupled system of Hadamard type fractional boundary value problems. By using the five functional fixed point theorem, the conditions for the existence of positive solutions are derived. Finally, to show the applicability of the main result, an illustrative example is also involved.

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Cite This Article

ÇERDİK, T. Ş. (2022). Analysis of a System of Nonlinear Hadamard Type Fractional Boundary Value Problems. Fundamental Journal of Mathematics and Applications, Cilt: 5 Sayı: 2, 114–126. https://ajindex.com/articles/905670

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References (16)

  1. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993
  2. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993
  3. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999
  4. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, In: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V, Amsterdam, 2006
  5. V. Lakshmikantham, S. Leela, J.V. Devi, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009
  6. J. R. Graef, L. Kong, Q. Kong, M. Wang, Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary condition, Fract. Calc. Appl. Anal., 15(3) (2012), 509-528
  7. A. Cabada, G. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Math. Anal. Appl., 389 (2012), 403-411
  8. J. Tariboon, S. Ntouyas, W. Sudsutad, Coupled systems of Riemann-Liouville fractional differential equations with Hadamard fractional integral boundary conditions, J. Nonlinear Sci. Appl., 9 (2016), 295-308
  9. J. He, M. Jia, X. Liu, H. Chen, Existence of positive solutions for a high order fractional differential equation integral boundary value problem with changing sign nonlinearity, Adv. Di er. Equ., 49 (2018)
  10. K. R. Prasad, M. Khuddush, P. Veeraiah, Countably many positive solutions for singular R-L fractional order bvp with R-S integral boundary conditions, Nonlinear Stud., 27(4) (2020), 1075-1089
  11. Z. B. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal., 72 (2010), 916-924
  12. T. S. Cerdik, F. Y. Deren, N. A. Hamal, Unbounded solutions for boundary value problems of Riemann Liouville fractional differential equations on the half-line, Fixed Point Theory, 19 (2018), 93-106
  13. F. Y. Deren, T. S. Cerdik, R. P. Agarwal, Existence criteria of positive solutions for fractional p-Laplacian boundary value problems, Filomat, 34(11) (2020)
  14. N. Nyamoradi, Multiple positive solutions for fractional differential systems, Ann. Univ. Ferrara, 58 (2012), 359-369
  15. S. Vong, Positive solutions of singular fractional differential equations with integral boundary conditions, Math. Comput. Model., 57(5-6) (2013), 1053-1059
  16. W. G. Yang, Y. P.