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Fractional Calculus and Applied Analysis

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Volume 18, Issue 4


Local Solvability of a Linear System with a Fractional Derivative in Time in a Boundary Condition

Nataliya Vasylyeva
  • Institute of Mathematics National Academy of Sciences of Ukraine Tereschenkivska, str. 3, Kiev - 4 – 01601, UKRAINE
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Published Online: 2015-08-04 | DOI: https://doi.org/10.1515/fca-2015-0058


In this paper we analyze a linear system for the Poisson equation with a boundary condition comprising the fractional derivative in time and the right-hand sides depended on time. First, we prove existence and uniqueness of the classical solution to this problem, and provide the coercive estimates of the solution. Second, based on the obtained results we establish one-to-one solvability to a linear system of a general form in the H¨older spaces.

Keywords: elliptic equation; fractional dynamic boundary condition; Caputo derivative; coercive estimates


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About the article

Received: 2015-01-08

Published Online: 2015-08-04

Published in Print: 2015-08-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 4, Pages 982–1005, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2015-0058.

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