Initial-value problems for linear distributed-order differential equations in Banach spaces

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dc.contributor.authorFedorov, Vladimir
dc.contributor.authorStreletskaya, Elizaveta
dc.date.accessioned2022-03-09T21:07:52Z
dc.date.available2022-03-09T21:07:52Z
dc.date.issued2018-10-30
dc.description.abstractWe solve the Cauchy problem for inhomogeneous distributed-order equations in a Banach space with a linear bounded operator in the right-hand side, with respect to the distributed Caputo derivative. First we find the solution by using the unique solvability theorem for the Cauchy problem. Then the results obtained are applied to the analysis of a distributed-order system of ordinary differential equations. Then we study an analogous equation, but with degenerate linear operator at the distributed derivative, which is called a degenerate equation. The pair of linear operators in the equation is assumed to be relatively bounded. For the two types of initial-value problems, we obtain the existence and uniqueness of a solution, and derive its form. Abstract results for the degenerate equations are used in the study of initial-boundary value problems with distributed order in time equations with polynomials of self-adjoint elliptic differential operator with respect to the spatial derivative.
dc.description.departmentMathematics
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationFedorov, V. E., & Streletskaya, E. M. (2018). Initial-value problems for linear distributed-order differential equations in Banach spaces. <i>Electronic Journal of Differential Equations, 2018</i>(176), pp. 1-17.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15472
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDistributed order differential equation
dc.subjectFractional Caputo derivative
dc.subjectDifferential equation in a Banach space
dc.subjectDegenerate evolution equation
dc.subjectCauchy problem
dc.titleInitial-value problems for linear distributed-order differential equations in Banach spaces
dc.typeArticle

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