One issue of future work is to develop the theory analysis of the method for the proposed fractional differential equation. The authors declare that there is no conflict of interests regarding the publication of this paper. National Center for Biotechnology Information , U. Journal List ScientificWorldJournal v. Published online Apr 1. Author information Article notes Copyright and License information Disclaimer.
Received Jan 9; Accepted Feb This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article has been cited by other articles in PMC.
Abstract This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. Introduction Fractional models have been increasingly shown by many scientists to describe adequately the problems with memory and nonlocal properties in fluid mechanics, viscoelasticity, physics, biology, chemistry, finance, and other areas of applications [ 1 — 6 ].
Notations and Some Preliminary Results In this section, we introduce some basic definitions and derive several preliminary results for developing the presented method.
The Composite Translated Sinc Functions The sinc functions and their properties are discussed in [ 23 , 24 ]. Numerical Examples To validate the effectiveness of the proposed method for problem 1 with 2 and 3 , we consider the example given in [ 16 ]. Open in a separate window. Figure 1. Figure 2. Figure 3. Figure 4.
Figure 5. Conclusion In this paper, we develop and analyze the efficient numerical methods for the fractional diffusion-wave equation.
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