Geodesic
An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 289-305.

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Summary: In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval $(0,1)$. An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.
Classification : 35R11, 65M06, 65M12
Keywords: Caputo derivative, fractional differential equation, subdiffusion, finite difference method, distributed order differential equation 
@article{ETNA_2015__44__a15,
     author = {Ford, N.J. and Morgado, M.L. and Rebelo, M.},
     title = {An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time},
     journal = {Electronic transactions on numerical analysis},
     pages = {289--305},
     publisher = {mathdoc},
     volume = {44},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a15/}
}
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Ford, N.J.; Morgado, M.L.; Rebelo, M. An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 289-305. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a15/