On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative

Samira Zerbib; Khalid Hilal; Ahmed Kajounı

doi:10.32323/ujma.1288015

EN

On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative

Abstract

This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results.

Keywords

Atangana-Baleanu-Caputo derivative, Fractional semi-linear differential equation, Krasnoselskii fixed point theorem, Resolvent family

Supporting Institution

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Project Number

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Thanks

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References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Samira Zerbib ^*
0000-0002-2782-0055
Morocco

Khalid Hilal
0000-0002-0806-2623
Morocco

Ahmed Kajounı
0000-0001-8484-6107
Morocco

Publication Date

September 30, 2023

Submission Date

April 26, 2023

Acceptance Date

September 23, 2023

Published in Issue

Year 2023 Volume: 6 Number: 3

DOI

https://doi.org/10.32323/ujma.1288015

IZ

https://izlik.org/JA43RR27UN

APA

Zerbib, S., Hilal, K., & Kajounı, A. (2023). On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative. Universal Journal of Mathematics and Applications, 6(3), 122-129. https://doi.org/10.32323/ujma.1288015

AMA

1.Zerbib S, Hilal K, Kajounı A. On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative. Univ. J. Math. Appl. 2023;6(3):122-129. doi:10.32323/ujma.1288015

Chicago

Zerbib, Samira, Khalid Hilal, and Ahmed Kajounı. 2023. “On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative”. Universal Journal of Mathematics and Applications 6 (3): 122-29. https://doi.org/10.32323/ujma.1288015.

EndNote

Zerbib S, Hilal K, Kajounı A (September 1, 2023) On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative. Universal Journal of Mathematics and Applications 6 3 122–129.

IEEE

[1]S. Zerbib, K. Hilal, and A. Kajounı, “On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative”, Univ. J. Math. Appl., vol. 6, no. 3, pp. 122–129, Sept. 2023, doi: 10.32323/ujma.1288015.

ISNAD

Zerbib, Samira - Hilal, Khalid - Kajounı, Ahmed. “On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative”. Universal Journal of Mathematics and Applications 6/3 (September 1, 2023): 122-129. https://doi.org/10.32323/ujma.1288015.

JAMA

1.Zerbib S, Hilal K, Kajounı A. On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative. Univ. J. Math. Appl. 2023;6:122–129.

MLA

Zerbib, Samira, et al. “On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative”. Universal Journal of Mathematics and Applications, vol. 6, no. 3, Sept. 2023, pp. 122-9, doi:10.32323/ujma.1288015.

Vancouver

1.Samira Zerbib, Khalid Hilal, Ahmed Kajounı. On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative. Univ. J. Math. Appl. 2023 Sep. 1;6(3):122-9. doi:10.32323/ujma.1288015