2016/04/23 by Khaled M. Furati, Furati, Khaled M., Olaniyi S. Iyiola +3
Mathematics · Engineering · #Fractional Differential Equations Solutions #Numerical methods in inverse problems #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1604.06886
We determine the space-dependent source term for a two-parameter fractional\ndiffusion problem subject to nonlocal non-self-adjoint boundary conditions and\ntwo local time-distinct datum. A bi-orthogonal pair of bases is used to\nconstruct a series representation of the solution and the source term. The two\nlocal time conditions spare us from measuring the fractional integral initial\nconditions commonly associated with fractional derivatives. On the other hand,\nthey lead to delicate 2\× 2 linear systems for the Fourier coefficients\nof the source term and of the fractional integral of the solution at t=0. The\nasymptotic behavior and estimates of the generalized Mittag-Leffler function\nare used to establish the solvability of these linear systems, and to obtain\nsufficient conditions for the existence of our construction. Analytical and\nnumerical examples are provided.\n