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Research Article | Open Access

Oscillation results for a nonlinear fractional differential equation

Paul Bosch1, José M. Rodríguez2, José M. Sigarreta3( )
Facultad de Ingeniería, Universidad del Desarrollo, Ave. Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago, Chile
Universidad Carlos III de Madrid, Departamento de Matemáticas, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
Universidad Autónoma de Guerrero, Centro Acapulco, CP 39610, Acapulco de Juárez, Guerrero, México
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Abstract

In this paper, the authors work with a general formulation of the fractional derivative of Caputo type. They study oscillatory solutions of differential equations involving these general fractional derivatives. In particular, they extend the Kamenev-type oscillation criterion given by Baleanu et al. in 2015. In addition, we prove results on the existence and uniqueness of solutions for many of the equations considered. Also, they complete their study with some examples.

Keywords

fractional derivatives and integralsfractional differential equationsoscillatory differential equations
CLC number: 26A33, 4K37

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 12486-12505
DOI: 10.3934/math.2023627

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Cite this article:
Bosch P, Rodríguez JM, Sigarreta JM. Oscillation results for a nonlinear fractional differential equation. AIMS Mathematics, 2023, 8(5): 12486-12505. https://doi.org/10.3934/math.2023627

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Received: 04 January 2023
Revised: 10 February 2023
Accepted: 20 February 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)