Initial value problems for fractional p-Laplacian equations with singularity

Mahir Hasanov; Mahir Hasanov

doi:10.3934/math.2024625

AIMS Mathematics

2024, Volume 9, Issue 5: 12800-12813. doi: 10.3934/math.2024625

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Research article

Initial value problems for fractional p-Laplacian equations with singularity

Mahir Hasanov ^,

Istanbul Beykent University, Faculty of Arts-Sciences, Department of Mathematics, Istanbul, Turkiye

Received: 19 February 2024 Revised: 23 March 2024 Accepted: 01 April 2024 Published: 03 April 2024
MSC : 26A33, 34A08, 34A12

We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper.
- initial value problems,
- Caputo fractional differential equations,
- fractional derivatives,
- fractional p-Laplacian,
- existence theorem
Citation: Mahir Hasanov. Initial value problems for fractional p-Laplacian equations with singularity[J]. AIMS Mathematics, 2024, 9(5): 12800-12813. doi: 10.3934/math.2024625

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Abstract

We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper.

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