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Journals / Results in Nonlinear Analysis / 2026 / Cilt: 5 Sayı: 2

On the existence of mild solutions for totally nonlinear Caputo-Hadamard fractional differential equations

Abdelouaheb Ardjouni(Souk Ahras University)
Abderrahim Guerfi(Annaba University)
Pages
161–168
Publication Date
2022-06-30
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AI Summary & Key Takeaways

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

Two example are given to illustrate our obtained results.

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🎯
Objective & Hypothesis:The existence of mild solutions of a totally nonlinear Caputo-Hadamard fractional differential equation is investigated using the Krasnoselskii-Burton fixed point theorem and some results are presented.
📊
Key Findings & Data:The existence of mild solutions of a totally nonlinear Caputo-Hadamard fractional differential equation is investigated using the Krasnoselskii-Burton fixed point theorem and some results are presented.
💡
Conclusion & Impact:Two example are given to illustrate our obtained results.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fractional differential equations · Krasnoselskii-Burton fixed point · Large contraction

Abstract

The existence of mild solutions of a totally nonlinear Caputo-Hadamard fractional differential equation is investigated using the Krasnoselskii-Burton fixed point theorem and some results are presented. Two example are given to illustrate our obtained results.

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Cite This Article

Ardjouni, A., Guerfi, A. (2022). On the existence of mild solutions for totally nonlinear Caputo-Hadamard fractional differential equations. Results in Nonlinear Analysis, Cilt: 5 Sayı: 2, 161–168. https://doi.org/10.53006/rna.1023029

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References (33)

  1. M. Adivar, Y.N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Di?erential Equations 2009(1) (2009), 1-20.
  2. B. Ahmad, S.K. Ntouyas, Existence and uniqueness of solutions for Caputo-Hadamard sequential fractional order neutral functional differential equations, Electronic Journal of Differential Equations 2017(36) (2017), 1-11.
  3. A. Ardjouni, Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations, Proyecciones 40(1) (2021), 139-152.
  4. A. Ardjouni, Asymptotic stability in Caputo-Hadamard fractional dynamic equations, Results in Nonlinear Analysis 4(2) (2021), 77-86.
  5. A. Ardjouni, Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions, AIMS Mathematics 4(4) (2019), 1101-1113.
  6. A. Ardjouni, A. Djoudi, Positive solutions for first-order nonlinear Caputo-Hadamard fractional relaxation differential equations, Kragujevac Journal of Mathematics 45(6) (2021), 897-908.
  7. A. Ardjouni, A. Djoudi, Initial-value problems for nonlinear hybrid implicit Caputo fractional differential equations, Malaya Journal of Matematik 7(2) (2019), 314-317.
  8. A. Ardjouni, A. Djoudi, Approximating solutions of nonlinear hybrid Caputo fractional integro-differential equations via Dhage iteration principle, Ural Mathematical Journal 5(1) 2019, 3-12.
  9. A. Ardjouni, A. Djoudi, Existence and uniqueness of positive solutions for first-order nonlinear Liouville-Caputo fractional differential equations, São Paulo J. Math. Sci. 14 (2020), 381-390.
  10. A. Ardjouni, A Djoudi, Existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional di?erential equations, Results in Nonlinear Analysis 2(3) (2019) 136-142.
  11. A. Ardjouni, A. Lachouri, A. Djoudi, Existence and uniqueness results for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations, Open Journal of Mathematical Analysis 3(2) (2019), 106-111.
  12. Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005) 495-505.
  13. Z.B. Bai, T.T. Qiu, Existence of positive solution for singular fractional differential equation, Appl. Math. Comput. 215 (2009), 2761-2767.
  14. H. Boulares, A. Ardjouni, Y. Laskri, Positive solutions for nonlinear fractional differential equations, Positivity 21 (2017), 1201?1212.
  15. B. Bordj, A. Ardjouni, Periodic and asymptotically periodic solutions in nonlinear coupled Volterra integro-dynamic systems with in nite delay on time scales, Advances in the Theory of Nonlinear Analysis and its Applications 5(2) (2021) 180-192.
  16. T.A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006.
  17. D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996), 609-625.
  18. C. Derbazi, Z. Baitiche, M. Benchohra, A. Cabada, Initial value problem for nonlinear fractional differential equations with ψ-Caputo derivative via monotone iterative technique, Axioms 9(57) (2020), 55-67.
  19. C. Derbazi, Z. Baitiche, M. Feckan, Some new uniqueness and Ulam stability results for a class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative using the Φ-fractional Bielecki-type norm, Turk. J. Math. 45 (2021), 2307-2322.
  20. C. Derbazi, Z. Baitiche, A. Zada, Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative, International Journal of Nonlinear Sciences and Numerical Simulation, https://doi.org/10.1515/ijnsns-2020-0228.
  21. E. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electron. J. Qual. Theory Differ. Equ. 3 (2008), 1-11.
  22. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Ams- terdam 2006.
  23. C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonlinear Anal. 74 (2011), 5975-5986.
  24. K.Q. Lan, W. Lin, Positive solutions of systems of Caputo fractional differential equations, Communications in Applied Analysis 17(1) (2013), 61-86.
  25. M. Matar, On existence of positive solution for initial value problem of nonlinear fractional differential equations of order 1 < α ≤ 2, Acta Math. Univ. Comenianae, LXXXIV(1) (2015), 51-57.
  26. K.S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New York, 1993.
  27. S. Niyom, S.K. Ntouyas, S. Laoprasittichok, J. Tariboon, Boundary value problems with four orders of Riemann-Liouville fractional derivatives, Adv. Difference Equ., 2016(165) (2016), 1-14.
  28. S.K. Ntouyas, J. Tariboon, Fractional boundary value problems with multiple orders of fractional derivatives and integrals, Electronic Journal of Differential Equations, 2017(100) (2017), 1-18.
  29. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  30. C. Wang, R. Wang, S. Wang, C. Yang, Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation, Bound. Value Probl. 2011 (2011), Art ID 297026.
  31. C. Wang, H. Zhang, S. Wang, Positive solution of a nonlinear fractional differential equation involving Caputo derivative, Discrete Dynamics in Natural and Society 2012 (2012), Art ID425408.
  32. S. Zhang, Existence results of positive solutions to boundary value problem for fractional differential equation, Positivity, 13(3) (2009), 583-599.
  33. S. Zhang, The existence of a positive solution for a fractional di?erential equation, J. Math. Anal. Appl. 252 (2000), 804-812.