In this paper we present and discuss a new numerical scheme for solving fractional delay differential equations of the generalform:$$D^{\beta}_{*}y(t)=f(t,y(t),y(t-\tau),D^{\alpha}_{*}y(t),D^{\alpha}_{*}y(t-\tau))$$on $a\leq t\leq b$,$0<\alpha\leq1$,$1<\beta\leq2$ and under the following interval and boundary conditions:\\$y(t)=\varphi(t) \qquad\qquad -\tau \leq t \leq a,$\\$y(b)=\gamma$\\where $D^{\beta}_{*}y(t)$,$D^{\alpha}_{*}y(t)$ and $D^{\alpha}_{*}y(t-\tau)$ are the standard Caputo fractional derivatives, $\varphi$ is the initial value and $\gamma$ is a smooth function.\\We also provide this method for solving some scientific models. The obtained results show that the propose method is veryeffective and convenient.
@article{25081,
title = {Modified finite difference method for solving fractional delay differential equations},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {35},
year = {2016},
doi = {10.5269/bspm.v35i2.25081},
language = {EN},
url = {http://dml.mathdoc.fr/item/25081}
}
Parsa Moghaddam, Behrouz; Salamat Mostaghim, Zeynab. Modified finite difference method for solving fractional delay differential equations. Boletim da Sociedade Paranaense de Matemática, Tome 35 (2016) . doi : 10.5269/bspm.v35i2.25081. http://gdmltest.u-ga.fr/item/25081/