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Year 2020, Volume: 3 Issue: 4, 133 - 137, 23.12.2020
https://doi.org/10.32323/ujma.647951

Abstract

References

  • [1] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.
  • [2] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [3] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [4] M. Caputo, Elasticita e Dissipazione, Zanichelli, Bologna, 1969.
  • [5] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 1-13.
  • [6] M.A. Refai, K. Pal, New aspects of Caputo-Fabrizio fractional derivative, Progr. Fract. Differ. Appl., 5 (2019), 157-166.
  • [7] T.M. Atanackovic, S. Pilipovic, D. Zorica, Properties of the Caputo-Fabrizio fractional derivative and its distributional settings, Frac. Calc. App. Anal., 21 (2018), 29-44.
  • [8] M. Caputo, M. Fabrizio, Applications of new time and spatial fractional derivatives with exponential kernels, Progr. Fract. Differ. Appl., 2 (2016), 1-11.
  • [9] D. B˘aleanu, S. Rezapour, Z. Saberpour, On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation, Boundary Value Problems, 219(79) (2019), 1-17.
  • [10] A. Shaikh, A. Tassaddiq, K.S. Nisar, D. Baleanu, Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations, Adv. Difference Equations, 2019(178) (2019), 1-14.
  • [11] S¸ . Toprakseven, The existence and uniqueness of initial-boundary value problems of the Caputo-Fabrizio differential equations, Universal J. Math. Appl., 2 (2019), 100-106.
  • [12] S. Zhang, L. Hu, S. Sun, The uniqueness of solution for initial value problems for fractional differential equations involving the Caputo-Fabrizio derivative, J. Nonlinear Sci. Appl., 11 (2018), 428-436.
  • [13] A. Cernea, On a Sturm-Liouville type differential inclusion of fractional order, Fract. Differ. Calc., 7 (2017) 385-393.
  • [14] J.P. Aubin, H. Frankowska, Set-valued Analysis, Birkhauser, Basel, 1990.
  • [15] D. O’ Regan, Fixed point theory for closed multifunctions, Arch. Math. (Brno), 34 (1998), 191-197.
  • [16] A. Bressan, G. Colombo, Extensions and selections of maps with decomposable values, Studia Math., 90 (1988), 69-86.
  • [17] A. Lasota, Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Math., Astronom. Physiques, 13 (1965), 781-786.
  • [18] M. Frignon, A. Granas, Theoremes d’existence pour les inclusions diff´erentielles sans convexite, C. R. Acad. Sci. Paris, Ser. I, 310 (1990), 819-822.
  • [19] H. Covitz, S.B. Nadler jr., Multivalued contraction mapping in generalized metric spaces, Israel J. Math., 8 (1970), 5-11.

A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type

Year 2020, Volume: 3 Issue: 4, 133 - 137, 23.12.2020
https://doi.org/10.32323/ujma.647951

Abstract

A fractional differential inclusion defined by Caputo-Fabrizio fractional derivative with bilocal boundary conditions is studied. A nonlinear alternative of Leray-Schauder type, Bressan-Colombo selection theorem for lower semicontinuous set-valued maps with decomposable values and Covitz-Nadler set-valued contraction principle are employed in order to obtain the existence of solutions when the set-valued map that define the problem has convex or non convex values.

References

  • [1] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.
  • [2] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [3] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [4] M. Caputo, Elasticita e Dissipazione, Zanichelli, Bologna, 1969.
  • [5] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 1-13.
  • [6] M.A. Refai, K. Pal, New aspects of Caputo-Fabrizio fractional derivative, Progr. Fract. Differ. Appl., 5 (2019), 157-166.
  • [7] T.M. Atanackovic, S. Pilipovic, D. Zorica, Properties of the Caputo-Fabrizio fractional derivative and its distributional settings, Frac. Calc. App. Anal., 21 (2018), 29-44.
  • [8] M. Caputo, M. Fabrizio, Applications of new time and spatial fractional derivatives with exponential kernels, Progr. Fract. Differ. Appl., 2 (2016), 1-11.
  • [9] D. B˘aleanu, S. Rezapour, Z. Saberpour, On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation, Boundary Value Problems, 219(79) (2019), 1-17.
  • [10] A. Shaikh, A. Tassaddiq, K.S. Nisar, D. Baleanu, Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations, Adv. Difference Equations, 2019(178) (2019), 1-14.
  • [11] S¸ . Toprakseven, The existence and uniqueness of initial-boundary value problems of the Caputo-Fabrizio differential equations, Universal J. Math. Appl., 2 (2019), 100-106.
  • [12] S. Zhang, L. Hu, S. Sun, The uniqueness of solution for initial value problems for fractional differential equations involving the Caputo-Fabrizio derivative, J. Nonlinear Sci. Appl., 11 (2018), 428-436.
  • [13] A. Cernea, On a Sturm-Liouville type differential inclusion of fractional order, Fract. Differ. Calc., 7 (2017) 385-393.
  • [14] J.P. Aubin, H. Frankowska, Set-valued Analysis, Birkhauser, Basel, 1990.
  • [15] D. O’ Regan, Fixed point theory for closed multifunctions, Arch. Math. (Brno), 34 (1998), 191-197.
  • [16] A. Bressan, G. Colombo, Extensions and selections of maps with decomposable values, Studia Math., 90 (1988), 69-86.
  • [17] A. Lasota, Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Math., Astronom. Physiques, 13 (1965), 781-786.
  • [18] M. Frignon, A. Granas, Theoremes d’existence pour les inclusions diff´erentielles sans convexite, C. R. Acad. Sci. Paris, Ser. I, 310 (1990), 819-822.
  • [19] H. Covitz, S.B. Nadler jr., Multivalued contraction mapping in generalized metric spaces, Israel J. Math., 8 (1970), 5-11.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Aurelian Cernea 0000-0002-9174-9855

Publication Date December 23, 2020
Submission Date November 18, 2019
Acceptance Date October 16, 2020
Published in Issue Year 2020 Volume: 3 Issue: 4

Cite

APA Cernea, A. (2020). A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Universal Journal of Mathematics and Applications, 3(4), 133-137. https://doi.org/10.32323/ujma.647951
AMA Cernea A. A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Univ. J. Math. Appl. December 2020;3(4):133-137. doi:10.32323/ujma.647951
Chicago Cernea, Aurelian. “A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type”. Universal Journal of Mathematics and Applications 3, no. 4 (December 2020): 133-37. https://doi.org/10.32323/ujma.647951.
EndNote Cernea A (December 1, 2020) A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Universal Journal of Mathematics and Applications 3 4 133–137.
IEEE A. Cernea, “A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type”, Univ. J. Math. Appl., vol. 3, no. 4, pp. 133–137, 2020, doi: 10.32323/ujma.647951.
ISNAD Cernea, Aurelian. “A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type”. Universal Journal of Mathematics and Applications 3/4 (December 2020), 133-137. https://doi.org/10.32323/ujma.647951.
JAMA Cernea A. A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Univ. J. Math. Appl. 2020;3:133–137.
MLA Cernea, Aurelian. “A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type”. Universal Journal of Mathematics and Applications, vol. 3, no. 4, 2020, pp. 133-7, doi:10.32323/ujma.647951.
Vancouver Cernea A. A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Univ. J. Math. Appl. 2020;3(4):133-7.

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