On the Nonlinear Integro-Differential Equations
The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s contracti...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/3/82 |
| _version_ | 1797519205841502208 |
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| author | Chenkuan Li Joshua Beaudin |
| author_facet | Chenkuan Li Joshua Beaudin |
| author_sort | Chenkuan Li |
| collection | DOAJ |
| description | The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s contractive principle, the multivariate Mittag–Leffler function and Babenko’s approach. We also provide a few examples to demonstrate the use of our main theorems by convolutions and the gamma function. |
| first_indexed | 2024-03-10T07:39:42Z |
| format | Article |
| id | doaj.art-77b68bb050e147479faebc0e797f16f4 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T07:39:42Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-77b68bb050e147479faebc0e797f16f42023-11-22T13:09:16ZengMDPI AGFractal and Fractional2504-31102021-07-01538210.3390/fractalfract5030082On the Nonlinear Integro-Differential EquationsChenkuan Li0Joshua Beaudin1Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, CanadaDepartment of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, CanadaThe goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s contractive principle, the multivariate Mittag–Leffler function and Babenko’s approach. We also provide a few examples to demonstrate the use of our main theorems by convolutions and the gamma function.https://www.mdpi.com/2504-3110/5/3/82Riemann–Liouville fractional integralLiouville–Caputo derivativeBabenko’s approachBanach fixed point theoremmultivariate Mittag–Leffler functiongamma function |
| spellingShingle | Chenkuan Li Joshua Beaudin On the Nonlinear Integro-Differential Equations Fractal and Fractional Riemann–Liouville fractional integral Liouville–Caputo derivative Babenko’s approach Banach fixed point theorem multivariate Mittag–Leffler function gamma function |
| title | On the Nonlinear Integro-Differential Equations |
| title_full | On the Nonlinear Integro-Differential Equations |
| title_fullStr | On the Nonlinear Integro-Differential Equations |
| title_full_unstemmed | On the Nonlinear Integro-Differential Equations |
| title_short | On the Nonlinear Integro-Differential Equations |
| title_sort | on the nonlinear integro differential equations |
| topic | Riemann–Liouville fractional integral Liouville–Caputo derivative Babenko’s approach Banach fixed point theorem multivariate Mittag–Leffler function gamma function |
| url | https://www.mdpi.com/2504-3110/5/3/82 |
| work_keys_str_mv | AT chenkuanli onthenonlinearintegrodifferentialequations AT joshuabeaudin onthenonlinearintegrodifferentialequations |