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Volume 4, Issue 2
Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for a Mixed Fractional Boundary Value Problem

Yani Liu & Qiaoluan Li

DOI: 10.12150/jnma.2022.207

J. Nonl. Mod. Anal., 4 (2022), pp. 207-219.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, a Lyapunov-type inequality for a linear differential equation involving right Riemann-Liouville and left Caputo fractional derivatives under Sturm-Liouville boundary conditions is established. Furthermore, the existence of solutions for the corresponding nonlinear differential equation is obtained by fixed point theorems.

  • Keywords

Fractional derivative, Lyapunov-type inequality, Fixed point theorem.

  • AMS Subject Headings

26A33, 34A40, 47H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-207, author = {Liu , Yani and Li , Qiaoluan}, title = {Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for a Mixed Fractional Boundary Value Problem}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {2}, pages = {207--219}, abstract = {

In this paper, a Lyapunov-type inequality for a linear differential equation involving right Riemann-Liouville and left Caputo fractional derivatives under Sturm-Liouville boundary conditions is established. Furthermore, the existence of solutions for the corresponding nonlinear differential equation is obtained by fixed point theorems.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.207}, url = {http://global-sci.org/intro/article_detail/jnma/20704.html} }
TY - JOUR T1 - Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for a Mixed Fractional Boundary Value Problem AU - Liu , Yani AU - Li , Qiaoluan JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 207 EP - 219 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.207 UR - https://global-sci.org/intro/article_detail/jnma/20704.html KW - Fractional derivative, Lyapunov-type inequality, Fixed point theorem. AB -

In this paper, a Lyapunov-type inequality for a linear differential equation involving right Riemann-Liouville and left Caputo fractional derivatives under Sturm-Liouville boundary conditions is established. Furthermore, the existence of solutions for the corresponding nonlinear differential equation is obtained by fixed point theorems.

Liu , Yani and Li , Qiaoluan. (2022). Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for a Mixed Fractional Boundary Value Problem. Journal of Nonlinear Modeling and Analysis. 4 (2). 207-219. doi:10.12150/jnma.2022.207
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