Browsing by Author "Heydari, Mohammad Hossein"

Now showing 1 - 2 of 2

Citation - WoS: 6
Citation - Scopus: 7
Chebyshev Cardinal Functions for a New Class of Nonlinear Optimal Control Problems With Dynamical Systems of Weakly Singular Variable-Order Fractional Integral Equations
(Sage Publications Ltd, 2020) Mahmoudi, Mohammad Reza; Avazzadeh, Zakieh; Baleanu, Dumitru; Heydari, Mohammad Hossein; 56389
The main objectives of this study are to introduce a new class of optimal control problems governed by a dynamical system of weakly singular variable-order fractional integral equations and to establish a computational method by utilizing the Chebyshev cardinal functions for their numerical solutions. In this way, a new operational matrix of variable-order fractional integration is generated for the Chebyshev cardinal functions. In the established method, first the control and state variables are approximated by the introduced basis functions. Then, the interpolation property of these basis functions together with their mentioned operational matrix is applied to derive an algebraic equation instead of the objective function and an algebraic system of equations instead of the dynamical system. Eventually, the constrained extrema technique is applied by adjoining the constraints generated from the dynamical system to the objective function using a set of Lagrange multipliers. The accuracy of the established approach is examined through several test problems. The obtained results confirm the high accuracy of the presented method.
Citation - WoS: 9
Citation - Scopus: 13
Orthonormal Piecewise Vieta-Lucas Functions for the Numerical Solution of the One- and Two-Dimensional Piecewise Fractional Galilei Invariant Advection-Diffusion Equations
(Elsevier, 2023) Razzaghi, Mohsen; Baleanu, Dumitru; Heydari, Mohammad Hossein; 56389
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement of the consideration problem alone. In defining this kind of derivatives, several types of fractional derivatives can be used simultaneously. Objectives: This study introduces a new kind of piecewise fractional derivative by employing the Caputo type distributed-order fractional derivative and ABC fractional derivative. The one-and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations are defined using this piecewise frac-tional derivative.Methods: A new class of basis functions called the orthonormal piecewise Vieta-Lucas (VL) functions are defined. Fractional derivatives of these functions in the Caputo and ABC senses are computed. These func-tions are utilized to construct two numerical methods for solving the introduced problems under non -local boundary conditions. The proposed methods convert solving the original problems into solving sys-tems of algebraic equations. Results: The accuracy and convergence order of the proposed methods are examined by solving several examples. The obtained results are investigated, numerically.Conclusion: This study introduces a kind of piecewise fractional derivative. This derivative is employed to define the one-and two-dimensional piecewise fractional Galilei invariant advection-diffusion equa-tions. Two numerical methods based on the orthonormal VL polynomials and orthonormal piecewise VL functions are established for these problems. The numerical results obtained from solving several examples confirm the high accuracy of the proposed methods.& COPY; 2022 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).