Geodesic
A linearized difference scheme for a class of fractional partial differential equations with delay
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 236-242

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A class of non linear fractional partial differential equations with initial and Dirichlet boundary conditions is under consideration. We seek to obtain numerical solutions for this considered class of equations based on finite difference method. The convergence order will be $2-\alpha$ in time and four in space. A numerical example is given to support the theoretical results.
Keywords: fractional partial differential equation, linear difference scheme, delay, discrete energy method, convergence analysis. 
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     title = {A linearized difference scheme for a class of fractional partial differential equations with delay},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a28/}
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A. S. Hendy. A linearized difference scheme for a class of fractional partial differential equations with delay. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 236-242. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a28/