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On some fractional differential inclusions with random parameters

  • Aurelian Cernea EMAIL logo
Veröffentlicht/Copyright: 13. März 2018
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 21 Heft 1

Abstract

We study some classes of fractional differential inclusions with random parameters and we establish Filippov’s type existence results in the case when the set-valued map has nonconvex values.

MSC 2010: Primary 34A60; Secondary 26A33
Key Words and Phrases: fractional differential inclusion; random parameters; Hilfer fractional derivative; measurable selection

References

[1] S. Abbas, W.A. Albarakati, M. Benchohra, J. Henderson, Existence and Ulam stabilities for Hadamard fractional integral equations with random effects. Electronic J. Diff. Equations2016, No 25 (2016), 1–12.Suche in Google Scholar

[2] S. Abbas, M. Benchohra, J.-E. Lazreg, G.M. N’Guérékata, Hilfer and Hadamard functional random fractional differential inclusions. CUBO (A Math. J.)19, No 1 (2017), 17–38; 10.4067/S0719-06462017000100002.Suche in Google Scholar

[3] S. Abbas, M. Benchohra, A. Petruşel, Ulam stability for Hilfer type fractional differential inclusions via the weakly Picard operators theory. Fract. Calc. Appl. Anal. 20, No 2 (2017), 384–398; 10.1515/fca-2017-0020; https://www.degruyter.com/view/j/fca.2017.20.issue-2/issue-files/fca.2017.20.issue-2.xml.Suche in Google Scholar

[4] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus: Models and Numerical Methods. Ser. on Complexity, Nonlinearity and Chaos, Vol. 3, World Scientific, Singapore (2012).10.1142/8180Suche in Google Scholar

[5] A.T. Bharucha-Reid, Random Integral Equations. Academic Press, New York (1972).Suche in Google Scholar

[6] C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions. Springer, Berlin (1977).10.1007/BFb0087685Suche in Google Scholar

[7] A. Cernea, On the existence of solutions for fractional differential inclusions with boundary conditions. Fract. Calc. Appl. Anal. 12, No 4 (2009), 433–442; at http://www.math.bas.bg/complan/fcaa/.Suche in Google Scholar

[8] A. Cernea, Filippov lemma for a class of Hadamard-type fractional differential inclusions. Fract. Calc. Appl. Anal. 18, No 1 (2015), 163–171; 10.1515/fca-2015-0011; https://www.degruyter.com/view/j/fca.2015.18.issue-1/issue-files/fca.2015.18.issue-1.xml.Suche in Google Scholar

[9] K. Diethelm, The Analysis of Fractional Differential Equations. Springer, Berlin (2010).10.1007/978-3-642-14574-2Suche in Google Scholar

[10] A.F. Filippov, Classical solutions of differential equations with multi-valued right hand side. SIAM J. Control5 (1967), 609–621.10.1137/0305040Suche in Google Scholar

[11] J. Hadamard, Essai sur l’étude des fonctions donnees par leur development de Taylor. J. Math. Pures Appl. 8 (1892), 101–186.Suche in Google Scholar

[12] R. Hilfer, Applications of Fractional Calculus in Physics. World Scientific, Singapore (2010).Suche in Google Scholar

[13] A.A. Kilbas, Hadamard-type fractional calculus. J. Korean Math. Soc. 38 (2001), 1191–1204.Suche in Google Scholar

[14] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applicationsof Fractional Differential Equations. Elsevier, Amsterdam (2006).Suche in Google Scholar

[15] J. Klafter, S.-C. Lim, R. Metzler, Fractional Calculus: Recent Advances. World Scientific, Singapore, 2011.10.1142/8087Suche in Google Scholar

[16] V. Lupulescu, S.K. Ntouyas, Random fractional differential equations. Int. J. Pure Appl. Math. 4 (2012), 119–136.Suche in Google Scholar

[17] M.D. Qassim, K.M. Furati, N. Tatar, On a differential equation involving Hilfer-Hadamard fractional derivative. Abstract Appl. Anal. 2012 (2012), ID 391062, 1–17.10.1155/2012/391062Suche in Google Scholar

[18] M.D. Qassim, N. Tatar, Well-posedness and stability for a differential problem with Hilfer-Hadamard fractional derivative Abstract Appl. Anal. 2013 (2013), ID 605029, 1–12.Suche in Google Scholar

[19] M. Yang, Q. Wang, Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions. Fract. Calc. Appl. Anal. 20, No 3 (2017), 679–705; 10.1515/fca-2017-0036; https://www.degruyter.com/view/j/fca.2017.20.issue-3/issue-files/fca.2017.20.issue-3.xml.Suche in Google Scholar

Received: 2017-10-24
Published Online: 2018-3-13
Published in Print: 2018-2-23

© 2018 Diogenes Co., Sofia

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
  8. Research Paper
  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
  10. Research Paper
  11. Some stability properties related to initial time difference for Caputo fractional differential equations
  12. Research Paper
  13. On an eigenvalue problem involving the fractional (s, p)-Laplacian
  14. Research Paper
  15. Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function
  16. Research Paper
  17. Time-fractional diffusion with mass absorption under harmonic impact
  18. Research Paper
  19. Optimal control of linear systems with fractional derivatives
  20. Research Paper
  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
  24. Research Paper
  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
  28. Research Paper
  29. Mittag-Leffler function and fractional differential equations
  30. Research Paper
  31. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point
  32. Research Paper
  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
https://doi.org/10.1515/fca-2018-0012
Schlagwörter für diesen Artikel
fractional differential inclusion; random parameters; Hilfer fractional derivative; measurable selection

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
  8. Research Paper
  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
  10. Research Paper
  11. Some stability properties related to initial time difference for Caputo fractional differential equations
  12. Research Paper
  13. On an eigenvalue problem involving the fractional (s, p)-Laplacian
  14. Research Paper
  15. Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function
  16. Research Paper
  17. Time-fractional diffusion with mass absorption under harmonic impact
  18. Research Paper
  19. Optimal control of linear systems with fractional derivatives
  20. Research Paper
  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
  24. Research Paper
  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
  28. Research Paper
  29. Mittag-Leffler function and fractional differential equations
  30. Research Paper
  31. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point
  32. Research Paper
  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
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