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### Stability Analysis of Some Fractional Differential Equations by Special type of Spline Function

Faraidun K. Hamasalh1 , Amina H. Ali1

1 Department Of Mathematic, Faculty of Science and Science Education, School of Science Education, Sulaimani University,
Kurdistan Region, Iraq.

Original: 29 May 2016, Revised: 5 August 2016, Accepted: 16 October 2016, Published online: 20 March 2017

DOI: https://doi.org/10.17656/jzs.10596

Abstract

One fractional spline interpolation is presented in this paper for the solution fractional initial value problems that is with spline interpolation as a new class depended on class splines as a method to approximate the exact solution of such problem. Error bounds were discussed as the presented spline function. On other hands, stability analysis has been accomplished and two examples were chosen as consideration for the numerical explanation of the presented technique. The outcome demonstrates that the presented fractional cubic spline function which interpolates the lacunary data acted as an efficient and effective way to solve such kind Special problems.

Key Words:
Fractional spline function
Caputo fractional derivative
Stability Analysis

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