THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS

Şuayip Toprakseven

THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS

Abstract

In this paper, a Lyapunov-type inequality and the existence of the positive solutions for boundary value problems of the nonlinear fractional Caputo-Fabrizio differential equation have been presented. By using the Guo Krasnoselskii’s fixed point theorem on cone and the properties of the associated Green`s function, we prove the existence of the positive solution. Finally, we gave some numerical examples to validate the theoretical findings.

Keywords

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Şuayip Toprakseven This is me
0000-0003-3901-9641
Türkiye

Publication Date

December 1, 2019

Submission Date

September 29, 2019

Acceptance Date

November 11, 2019

Published in Issue

Year 2019 Volume: 37 Number: 4

IZ

https://izlik.org/JA98DG37JW

Cite

RIS / Bibtex

APA

Toprakseven, Ş. (2019). THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS. Sigma Journal of Engineering and Natural Sciences, 37(4), 1129-1137. https://izlik.org/JA98DG37JW

AMA

1.Toprakseven Ş. THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS. SIGMA. 2019;37(4):1129-1137. https://izlik.org/JA98DG37JW

Chicago

Toprakseven, Şuayip. 2019. “THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS”. Sigma Journal of Engineering and Natural Sciences 37 (4): 1129-37. https://izlik.org/JA98DG37JW.

EndNote

Toprakseven Ş (December 1, 2019) THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS. Sigma Journal of Engineering and Natural Sciences 37 4 1129–1137.

IEEE

[1]Ş. Toprakseven, “THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS”, SIGMA, vol. 37, no. 4, pp. 1129–1137, Dec. 2019, [Online]. Available: https://izlik.org/JA98DG37JW

ISNAD

Toprakseven, Şuayip. “THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS”. Sigma Journal of Engineering and Natural Sciences 37/4 (December 1, 2019): 1129-1137. https://izlik.org/JA98DG37JW.

JAMA

1.Toprakseven Ş. THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS. SIGMA. 2019;37:1129–1137.

MLA

Toprakseven, Şuayip. “THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 4, Dec. 2019, pp. 1129-37, https://izlik.org/JA98DG37JW.

Vancouver

1.Şuayip Toprakseven. THE EXISTENCE OF POSITIVE SOLUTIONS AND A LYAPUNOV TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS OF THE FRACTIONAL CAPUTO-FABRIZIO DIFFERENTIAL EQUATIONS. SIGMA [Internet]. 2019 Dec. 1;37(4):1129-37. Available from: https://izlik.org/JA98DG37JW