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

Aurelian Cernea

doi:10.32323/ujma.647951

EN

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

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.

Keywords

Differential inclusion, Fixed point, Fractional derivative, Selection

References

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[2] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
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[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.
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[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.
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[13] A. Cernea, On a Sturm-Liouville type differential inclusion of fractional order, Fract. Differ. Calc., 7 (2017) 385-393.
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[15] D. O’ Regan, Fixed point theory for closed multifunctions, Arch. Math. (Brno), 34 (1998), 191-197.
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[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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Aurelian Cernea ^*
0000-0002-9174-9855
Romania

Publication Date

December 23, 2020

Submission Date

November 18, 2019

Acceptance Date

October 16, 2020

Published in Issue

Year 2020 Volume: 3 Number: 4

DOI

https://doi.org/10.32323/ujma.647951

IZ

https://izlik.org/JA27AU26XU

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

1.Cernea A. A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Univ. J. Math. Appl. 2020;3(4):133-137. doi:10.32323/ujma.647951

Chicago

Cernea, Aurelian. 2020. “A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type”. Universal Journal of Mathematics and Applications 3 (4): 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

[1]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, Dec. 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 1, 2020): 133-137. https://doi.org/10.32323/ujma.647951.

JAMA

1.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, Dec. 2020, pp. 133-7, doi:10.32323/ujma.647951.

Vancouver

1.Aurelian Cernea. A Bilocal Problem Associated to a Fractional Differential Inclusion of Caputo-Fabrizio Type. Univ. J. Math. Appl. 2020 Dec. 1;3(4):133-7. doi:10.32323/ujma.647951