Numerical Solutions for Linear Fractional Differential Equations of Order \(1 < \alpha< 2\) Using Finite Difference Method (ffdm)

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Authors
Ramzi B. Albadarneh
 Department of Mathematics, Hashemite University, Zarqa Jordan.
Iqbal M. Batiha
 Department of Mathematics, Al alBayt University, MafraqJordan.
Mohammad Zurigat
 Department of Mathematics, Al alBayt University, MafraqJordan.
Abstract
The major goal of this paper is to find accurate solutions for linear fractional differential equations
of order \(1 < \alpha < 2\) . Hence, it is necessary to carry out this goal by preparing a new method called
Fractional Finite Difference Method (FFDM). However, this method depends on several important
topics and definitions such as Caputo's definition as a definition of fractional derivative, Finite
Difference Formulas in three types (Forward, Central and Backward) for approximating the second
and third derivatives and Composite Trapezoidal Rule for approximating the integral term in the
Caputo's definition. In this paper, the numerical solutions of linear fractional differential equations
using FFDM will be discussed and illustrated. The purposed problem is to construct a method
to find accurate approximate solutions for linear fractional differential equations. The efficiency of
FFDM will be illustrated by solving some problems of linear fractional differential equations of order
\(1 < \alpha< 2\).
Keywords
 Finite difference formulas
 composite trapezoidal rule
 numerical solutions
 linear fractional differential equation.
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