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Volume 4, Issue 1 (8-2018)
Abstract
Fractional differential equations (FDEs) have attracted in the recent years a considerable interest due to their frequent appearance in various fields and their more accurate models of systems under consideration provided by fractional derivatives. For example, fractional derivatives have been used successfully to model frequency dependent damping behavior of many viscoelastic materials. They are also used in modeling of many chemical processed, mathematical biology and many other problems in engineering. The history and a comprehensive treatment of FDEs are provided by Podlubny and a review of some applications of FDEs are given by Mainardi.
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Dr. Somayeh Nemati, Zahra Rezaei Kalansara,
Volume 9, Issue 4 (12-2023)
Abstract
In this paper, using a new method based on the generalized hat functions, we solve a class of fractional delay differential equations in which the fractional derivative is considered in the sense of Caputo. First, we introduce the generalized hat functions and their corresponding operational matrices. Then, in order to solve the considered problem, the existing functions are approximated using the basis functions. By employing the properties of generalized hat functions, the Caputo fractional derivative and the Riemann-Liouville fractional integral, a system of algebraic equations is obtained which by solving it, the unknown coefficients are determined. By substituting the resulting values, an approximation of the solution of the problem is obtained. In addition, the computational complexity of the resulting system is investigated. In continue, an error analysis of the method is given. Finally, the accuracy and efficiency of the proposed method are shown by presenting two examples.
Hamid Reza Marzban, Atiyeh Nezami,
Volume 9, Issue 4 (12-2023)
Abstract
In this research, an efficient numerical method is presented for solving a class of nonlinear delay fractional optimal control problems with inequality constraints on the state and control variables. The proposed approach is based on the hybrid of block-pulse functions and fractional-order Legendre functions. By using the operational matrices of delay and derivative associated with the hybrid functions, the original optimal control problem is transformed into a parameter optimization one. The numerical results, demonstrate the accuracy and validity of the suggested method.
