# Solving Fractional Variational Problem Via an Orthonormal Function

• Akram kheirabadi Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand
• Asadollah Mahmoudzadeh Vaziri Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand
• Sohrab Effati Department of Applied Mathematics, Faculty of Mathematical Sciences, Fer- dowsi University of Mashhad, Mashhad
Keywords: Fractional optimal control, Sine-Cosine wavelet, Operational matrix, Hat function

### Abstract

In the present paper, a direct numerical technique for solving fractional optimal control problems based on an orthonormal wavelet, is introduced. First we approximate the involved functions by Sine-Cosine wavelet basis; then, an operational matrix is used to transform the given problem into a linear system of algebraic equations, which is easier. In fact operational matrix of Riemann-Liouville fractional integration and derivative of Sine-Cosine wavelet are employed to achieve a linear algebraic equation. The mentioned matrices are derived via hat functions. The solution of transformed system, gives us the solution of original problem. Two numerical examples are also given. Finally, the paper is ended with conclusion

### Author Biographies

Akram kheirabadi, Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand
PHD student
Asadollah Mahmoudzadeh Vaziri, Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand
Assistant Professor

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Published
2019-05-19
How to Cite
kheirabadi, A., Mahmoudzadeh Vaziri, A., & Effati, S. (2019). Solving Fractional Variational Problem Via an Orthonormal Function. Statistics, Optimization & Information Computing, 7(2), 447-455. https://doi.org/10.19139/soic.v7i2.502
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Research Articles