A Cauchy type problem for a degenerate equation with the Riemann-Liouville derivative in the sectorial case

DOI10.1134/S0037446619020162zbMath1419.34018WikidataQ127971163 ScholiaQ127971163MaRDI QIDQ2313310

Anna S. Avilovich, Vladimir Evgenyevich Fedorov

Publication date: 18 July 2019

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

sectorial operatorRiemann-Liouville fractional derivativeCauchy type problemdegenerate evolution equationdifferential equation in Banach spacefractional order equation

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Linear differential equations in abstract spaces (34G10) Fractional ordinary differential equations (34A08)

Related Items (11)

The defect of a Cauchy type problem for linear equations with several Riemann-Liouville derivatives ⋮ On multiplicative perturbations of abstract degenerate fractional differential equations ⋮ Complex powers of fractional sectorial operators and quasilinear equations with Riemann-Liouville derivatives ⋮ Nonlocal solvability of quasilinear degenerate equations with Gerasimov-Caputo derivatives ⋮ Degenerate equations with the Dzhrbashyan-Nersesyan derivative in the sectorial case ⋮ Multi-term equations with Riemann-Liouville derivatives and Hölder type function spaces ⋮ Initial value problems for some classes of linear evolution equations with several fractional derivatives ⋮ Semilinear fractional-order evolution equations of Sobolev type in the sectorial case ⋮ Unnamed Item ⋮ The Cauchy problem for a class of multi-term equations with Gerasimov-Caputo derivatives ⋮ Sectorial tuples of operators and quasilinear fractional equations with multi-term linear part

Cites Work

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• Sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi-controls
• Solutions for initial boundary value problems for some degenerate equations systems of fractional order with respect to the time
• Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative
• Distributed control problems for a class of degenerate semilinear evolution equations
• Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions
• Quasilinear equations that are not solved for the higher-order time derivative
• Equations in Banach spaces with a degenerate operator under a fractional derivative
• On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives
• Geometric theory of semilinear parabolic equations
• Degenerate linear evolution equations with the Riemann-Liouville fractional derivative
• Disjoint hypercyclic and disjoint topologically mixing properties of degenerate fractional differential equations
• Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions
• Abstract time-fractional equations: existence and growth of solutions
• Resolving operators of degenerate evolution equations with fractional derivative with respect to time
• Abstract multi-term fractional differential equations
• Evolutionary Integral Equations and Applications
• Strong Solutions to Nonlinear Degenerate Fractional Order Evolution Equations
• Degenerate fractional differential equations in locally convex spaces with a $\sigma$-regular pair of operators
• Analytic in a Sector Resolving Families of Operators for Degenerate Evolution Fractional Equations

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