Oscillation results for a nonlinear fractional differential equation

Paul Bosch; José M. Rodríguez; José M. Sigarreta; Paul Bosch; José M. Rodríguez; José M. Sigarreta

doi:10.3934/math.2023627

AIMS Mathematics

2023, Volume 8, Issue 5: 12486-12505. doi: 10.3934/math.2023627

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Research article

Oscillation results for a nonlinear fractional differential equation

1.
Facultad de Ingeniería, Universidad del Desarrollo, Ave. Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago, Chile
2.
Universidad Carlos III de Madrid, Departamento de Matemáticas, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
3.
Universidad Autónoma de Guerrero, Centro Acapulco, CP 39610, Acapulco de Juárez, Guerrero, México

Received: 04 January 2023 Revised: 10 February 2023 Accepted: 20 February 2023 Published: 27 March 2023
MSC : 26A33, 4K37

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.
- fractional derivatives and integrals,
- fractional differential equations,
- oscillatory differential equations
Citation: Paul Bosch, José M. Rodríguez, José M. Sigarreta. Oscillation results for a nonlinear fractional differential equation[J]. AIMS Mathematics, 2023, 8(5): 12486-12505. doi: 10.3934/math.2023627

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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.

References

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