Geodesic
Numerical solution for a variable-order fractional nonlinear cable equation via Chebyshev cardinal functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12

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In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique. 
@article{ZVMMF_2017_57_12_a10,
     author = {Somayeh Abdi-Mazraeh and Safar Irandoust-Pakchin and Ali Khani},
     title = {Numerical solution for a variable-order fractional nonlinear cable equation via {Chebyshev} cardinal functions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2098},
     publisher = {mathdoc},
     volume = {57},
     number = {12},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a10/}
}
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Somayeh Abdi-Mazraeh; Safar Irandoust-Pakchin; Ali Khani. Numerical solution for a variable-order fractional nonlinear cable equation via Chebyshev cardinal functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a10/