Diyala Journal for Pure Science
Scientific Refereed Journal Published By College of Science - University of Diyala
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Diyala Journal For Pure Sciences DJPS
ISRA Impact Factor:3.715
P- ISSN:2222-8373, E-ISSN:2518-9255
Volume 14, Issue 2 , April . 2018
Solving Fractional Initial Value Problems by Using Hybrid Series
Saad Naji Al-Azzawi , Ronak Bagelany , Ahmed Murshed
Year: 2018, Volume: 14, Issue: 2
Pages: 106-121, DOI: http://dx.doi.org/10.24237/djps.1402.385C
In this paper, we suggest a new method for solving fractional initial value problems of different fractional orders. We call it hybrid Series Solution (Fractional with power, Fractional with fractional, Fractional with power and fractional). The main difference between Caputo and Riemann – Liouville formulas for the fractional derivatives as mentioned. The paper focuses on finding the exact solution of Bagley-Torvik equation and other nonhomogeneous fractional differential equations, illustrated by some Theorems and examples.
Key words: Hybrid Series, Bagley-Torvik equation, Fractional Calculus, Caputo and Riemann - Liouville derivatives.