Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition

Timurkhan S. Aleroev, Mokhtar Kirane, Salman A. Malik

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57 Scopus citations

Abstract

We consider a linear heat equation involving a fractional derivative in time, with a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution for a problem with an over-determining condition of integral type. We prove the existence and uniqueness of the solution, and its continuous dependence on the data.

Original languageBritish English
Article number270
JournalElectronic Journal of Differential Equations
Volume2013
StatePublished - 6 Dec 2013

Keywords

  • Bi-orthogonal system of functions
  • Fourier series
  • Fractional derivative
  • Heat equation
  • Integral equations
  • Inverse problem

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