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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.<\/jats:p>","DOI":"10.3390\/axioms11030096","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T21:11:07Z","timestamp":1645737067000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Class of Quasilinear Equations with Riemann\u2013Liouville Derivatives and Bounded Operators"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0787-3272","authenticated-orcid":false,"given":"Vladimir E.","family":"Fedorov","sequence":"first","affiliation":[{"name":"Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia"},{"name":"Laboratory of Functional Materials, South Ural State University (National Research University), Lenin Av., 76, 454080 Chelyabinsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4075-5099","authenticated-orcid":false,"given":"Mikhail M.","family":"Turov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bui Trong","family":"Kien","sequence":"additional","affiliation":[{"name":"Department 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, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,24]]},"reference":[{"key":"ref_1","unstructured":"Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers."},{"key":"ref_2","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_3","unstructured":"Nakhushev, A.M. (2003). Fractional Calculus and Its Applications, Fizmatlit. (In Russian)."},{"key":"ref_4","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science Publishing."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kosti\u0107, M. (2015). Abstract Volterra Integro-Differential Equations, CRC Press.","DOI":"10.1201\/b18463"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Tarasov, V.E. (2011). Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer.","DOI":"10.1007\/978-3-642-14003-7"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Uchaykin, V.V. (2012). Fractional Derivatives for Physicists and Engineers, Higher Education Press.","DOI":"10.1007\/978-3-642-33911-0_4"},{"key":"ref_8","first-page":"85","article-title":"Initial value problems for some classes of linear evolution equations with several fractional derivatives","volume":"28","author":"Fedorov","year":"2021","journal-title":"Math. Notes NEFU"},{"key":"ref_9","first-page":"41","article-title":"Nonlinear equations with degenerate operator at fractional Caputo derivative","volume":"40","author":"Plekhanova","year":"2016","journal-title":"Math. Methods Appl. 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Elliptic Equ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11961","DOI":"10.1002\/mma.6794","article-title":"A class of inverse problems for evolution equations with the Riemann\u2013Liouville derivative in the sectorial case","volume":"44","author":"Fedorov","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1134\/S0037446621050141","article-title":"The defect of a Cauchy type problem for linear equations with several Riemann\u2013Liouville derivatives","volume":"62","author":"Fedorov","year":"2021","journal-title":"Sib. Math. J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fedorov, V.E., Du, W.-S., and Turov, M.M. (2022). On the unique solvability of incomplete Cauchy type problems for a class of multi-term equations with the Riemann\u2013Liouville derivatives. Symmetry, 14.","DOI":"10.3390\/sym14010075"},{"key":"ref_16","unstructured":"Triebel, H. (1978). 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Theory and Applications of Hopf Bifurcation, Cambridge University Press."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/3\/96\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:27:01Z","timestamp":1760135221000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/3\/96"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,24]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["axioms11030096"],"URL":"https:\/\/doi.org\/10.3390\/axioms11030096","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,24]]}}}