| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 767037 | Communications in Nonlinear Science and Numerical Simulation | 2012 | 7 Pages |
Abstract
A new fractional derivative of the Grüwald–Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Grüwald–Letnikov and the two-sided fractional derivatives. Several properties of such generalized operator are presented, and some particular cases deduced.
► The new derivative of the incremental ratio type incorporates 4 existing fractional derivatives. ► It leads to a general integral representation having the Liouville and Riesz integrals as special cases. ► It allows us writing the partial differential equations with a unique derivative formulation. ► It exists for a wide class of functions. ► It is suitable for numerical implementations.
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Authors
Manuel D. Ortigueira, Juan J. Trujillo,