An inverse source problem for a two-parameter anomalous diffusion with local time datum

作者：Furati Khaled M^*; Iyiola Olaniyi S; Mustapha Kassem

来源：Computers & Mathematics with Applications, 2017, 73(6): 1008-1015.

DOI：10.1016/j.camwa.2016.06.036

• Inverse source problem
• Fractional diffusion
• Mittag-Leffler function
• Hilfer derivative

We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a series representation of the solution and the source term. The two local time conditions spare us from measuring the fractional integral initial conditions commonly associated with fractional derivatives. On the other hand, they lead to delicate 2 x 2 linear systems for the Fourier coefficients of the source term and of the fractional integral of the solution at t = 0. The asymptotic behavior and estimates of the generalized Mittag-Leffler function are used to establish the solvability of these linear systems, and to obtain sufficient conditions for the existence of our construction.

• 出版日期2017-3-15
• 单位中国石油大学（北京）