A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators
The existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them. Nonlinearity in the equation is assumed to be Lipschitz con...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-02-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/3/96 |
| _version_ | 1797472862388355072 |
|---|---|
| author | Vladimir E. Fedorov Mikhail M. Turov Bui Trong Kien |
| author_facet | Vladimir E. Fedorov Mikhail M. Turov Bui Trong Kien |
| author_sort | Vladimir E. Fedorov |
| collection | DOAJ |
| description | The existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them. Nonlinearity in the equation is assumed to be Lipschitz continuous and dependent on lower order fractional derivatives, which orders have the same fractional part as the order of the highest fractional derivative. The obtained abstract result is applied to study a class of initial-boundary value problems to time-fractional order equations with polynomials of an elliptic self-adjoint differential operator with respect to spatial variables as linear operators at the time-fractional derivatives. The nonlinear operator in the considered partial differential equations is assumed to be smooth with respect to phase variables. |
| first_indexed | 2024-03-09T20:07:09Z |
| format | Article |
| id | doaj.art-d3c8a62027bb4bbfa709ce8d9fd25a92 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T20:07:09Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-d3c8a62027bb4bbfa709ce8d9fd25a922023-11-24T00:28:45ZengMDPI AGAxioms2075-16802022-02-011139610.3390/axioms11030096A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded OperatorsVladimir E. Fedorov0Mikhail M. Turov1Bui Trong Kien2Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, RussiaDepartment of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, RussiaDepartment of Optimization and Control Theory, Institute of Mathematics of the Vietnam Academy of Sciences and Technologies, 8 Hoang Quoc Viet Road, Caugiay District, Hanoi 10307, VietnamThe existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them. Nonlinearity in the equation is assumed to be Lipschitz continuous and dependent on lower order fractional derivatives, which orders have the same fractional part as the order of the highest fractional derivative. The obtained abstract result is applied to study a class of initial-boundary value problems to time-fractional order equations with polynomials of an elliptic self-adjoint differential operator with respect to spatial variables as linear operators at the time-fractional derivatives. The nonlinear operator in the considered partial differential equations is assumed to be smooth with respect to phase variables.https://www.mdpi.com/2075-1680/11/3/96multi-term fractional differential equationquasilinear equationRiemann–Liouville fractional derivativedefect of Cauchy type problemfixed point theoreminitial-boundary value problem |
| spellingShingle | Vladimir E. Fedorov Mikhail M. Turov Bui Trong Kien A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators Axioms multi-term fractional differential equation quasilinear equation Riemann–Liouville fractional derivative defect of Cauchy type problem fixed point theorem initial-boundary value problem |
| title | A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators |
| title_full | A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators |
| title_fullStr | A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators |
| title_full_unstemmed | A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators |
| title_short | A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators |
| title_sort | class of quasilinear equations with riemann liouville derivatives and bounded operators |
| topic | multi-term fractional differential equation quasilinear equation Riemann–Liouville fractional derivative defect of Cauchy type problem fixed point theorem initial-boundary value problem |
| url | https://www.mdpi.com/2075-1680/11/3/96 |
| work_keys_str_mv | AT vladimirefedorov aclassofquasilinearequationswithriemannliouvillederivativesandboundedoperators AT mikhailmturov aclassofquasilinearequationswithriemannliouvillederivativesandboundedoperators AT buitrongkien aclassofquasilinearequationswithriemannliouvillederivativesandboundedoperators AT vladimirefedorov classofquasilinearequationswithriemannliouvillederivativesandboundedoperators AT mikhailmturov classofquasilinearequationswithriemannliouvillederivativesandboundedoperators AT buitrongkien classofquasilinearequationswithriemannliouvillederivativesandboundedoperators |