Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives

Hamza Tabti; Fahd Jarad

doi:10.32323/ujma.1691155

Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives

Abstract

Our aim in this paper is to explore the existence of nonnegative solutions for a boundary value problem involving nonlinear Caputo fractional differential equations. The analysis begins with the formulation of superlinear and sublinear conditions, under which the Guo-Krasnosel'skii fixed point theorem is applied in a cone to get the existence of positive solutions. To facilitate this, the corresponding Green's function is constructed, and its essential properties are explored. A number of illustrative examples are included to show the applicability of the theoretical results and emphasize their effectiveness.

Keywords

Caputo, Existence, Fixed point theorem, Fractional differential equation, Green, Sublinear condition, Superlinear condition

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Hamza Tabti ^*
0000-0003-3245-873X
Algeria

Fahd Jarad
0000-0002-3303-0623
Türkiye

Early Pub Date

September 15, 2025

Publication Date

September 17, 2025

Submission Date

May 4, 2025

Acceptance Date

September 12, 2025

Published in Issue

Year 2025 Volume: 8 Number: 3

DOI

https://doi.org/10.32323/ujma.1691155

IZ

https://izlik.org/JA27GA89FX

APA

Tabti, H., & Jarad, F. (2025). Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives. Universal Journal of Mathematics and Applications, 8(3), 158-166. https://doi.org/10.32323/ujma.1691155

AMA

1.Tabti H, Jarad F. Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives. Univ. J. Math. Appl. 2025;8(3):158-166. doi:10.32323/ujma.1691155

Chicago

Tabti, Hamza, and Fahd Jarad. 2025. “Existence of Solutions for a Class of Nonlinear Boundary Value Problems With Caputo Fractional Derivatives”. Universal Journal of Mathematics and Applications 8 (3): 158-66. https://doi.org/10.32323/ujma.1691155.

EndNote

Tabti H, Jarad F (September 1, 2025) Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives. Universal Journal of Mathematics and Applications 8 3 158–166.

IEEE

[1]H. Tabti and F. Jarad, “Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives”, Univ. J. Math. Appl., vol. 8, no. 3, pp. 158–166, Sept. 2025, doi: 10.32323/ujma.1691155.

ISNAD

Tabti, Hamza - Jarad, Fahd. “Existence of Solutions for a Class of Nonlinear Boundary Value Problems With Caputo Fractional Derivatives”. Universal Journal of Mathematics and Applications 8/3 (September 1, 2025): 158-166. https://doi.org/10.32323/ujma.1691155.

JAMA

1.Tabti H, Jarad F. Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives. Univ. J. Math. Appl. 2025;8:158–166.

MLA

Tabti, Hamza, and Fahd Jarad. “Existence of Solutions for a Class of Nonlinear Boundary Value Problems With Caputo Fractional Derivatives”. Universal Journal of Mathematics and Applications, vol. 8, no. 3, Sept. 2025, pp. 158-66, doi:10.32323/ujma.1691155.

Vancouver

1.Hamza Tabti, Fahd Jarad. Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives. Univ. J. Math. Appl. 2025 Sep. 1;8(3):158-66. doi:10.32323/ujma.1691155