On a Sequential Fractional Differential Inclusion with Nonlocal Integro-Multipoint Boundary Conditions

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  • Aurelian Cernea,

Published in Issue 2025-11-09

How to Cite

On a Sequential Fractional Differential Inclusion with Nonlocal Integro-Multipoint Boundary Conditions. (2025). Communications in Nonlinear Analysis, 12(2). https://oiccpress.com/cna/article/view/17882

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Abstract

It is considered a sequential fractional differential inclusion with nonlocal integro-multipoint boundary conditions defined by a set-valued map with nonconvex values. An existence result and a topological property of its solution set are proved.

Keywords

  • differential inclusion,
  • fractional derivative,
  • boundary value problem
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References

  1. [1] Ahmad B., Alruwaily Y., Alsaedi A., Ntouyas S.K. Sequential fractional differential equations with nonlocal integro-multipoint boundary conditions. Novi Sad J. Math. 53 (2023), 143–63.
  2. [2] Aubin J.P., Frankowska H. Set-Valued Analysis. Birkhauser, Basel, 1990.
  3. [3] Baleanu D., Diethelm K., Scalas E., Trujillo J.J. Fractional Calculus Models and Numerical Methods. World Scientific, Singapore, 2012.
  4. [4] Caputo M. Elasticita e Dissipazione. Zanichelli, Bologna, 1969.
  5. [5] Cernea A. Some remarks on a fractional differential inclusion with non-separated boundary conditions. Electronic J. Qual. Theory Differ. Equa. 2011(54), 1–14.
  6. [6] Cernea A. Some remarks on a multi point boundary value problem for a fractional order differential inclusion. J. Appl. Nonlin. Dyn. 2 (2013), 151–160.
  7. [7] Cernea A. On a fractional differential inclusion with mixed boundary conditions. Nonlinear Stud. 29 (2022), 1281–1290.
  8. [8] Cernea A. On a fractional differential inclusion involving a generalized Caputo type derivative with certain fractional integral boundary conditions. J. Frac. Calc. Nonlin. Syst. 3 (2022), 1–11.
  9. [9] Diethelm K. The Analysis of Fractional Differential Equations. Springer, Berlin, 2010.
  10. [10] Filippov A.F. Classical solutions of differential equations with multivalued right hand side. SIAM J. Control. 5 (1967), 609–621.
  11. [11] Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
  12. [12] Kuratowski K., Ryll-Nardzewski C. A general theorem on selectors. Bull. Acad. Pol. Sci. 13 (1965), 397–403.
  13. [13] Marano S. Fixed points of multivalued contractions with nonclosed, nonconvex values. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 5 (1994), 203–212.
  14. [14] Marano S., Staicu V. On the set of solutions to a class of nonconvex nonclosed differential inclusions. Acta Math. Hungar. 76 (1997), 287–301.
  15. [15] Podlubny I. Fractional Differential Equations. Academic Press, San Diego, 1999.