On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operators

  • Praveen AgarwalEmail author
  • Erkinjon Karimov
  • Murat Mamchuev
  • Michael Ruzhansky
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of solutions to formulated problems in terms of multinomial Mittag-Leffler and first kind Bessel functions.



This work was done during the visit of authors to ICMS in Edinburgh in July 2016 and was supported by “Research in Group” activity of ICMS. The last author was also supported in part by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Praveen Agarwal
    • 1
    Email author
  • Erkinjon Karimov
    • 2
  • Murat Mamchuev
    • 3
  • Michael Ruzhansky
    • 4
  1. 1.Department of MathematicsAnand International College of EngineeringJaipurIndia
  2. 2.Institute of Mathematics named after V.I. RomanovskyAcademy of Sciences of the Republic of UzbekistanTashkentUzbekistan
  3. 3.Department of Fractional CalculusInstitute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RASNalchikRussia
  4. 4.Department of MathematicsImperial College LondonLondonUK

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