American Journal of Theoretical and Applied Statistics
Volume 6, Issue 5-1, September 2017, Pages: 46-50
Received: Mar. 15, 2017;
Accepted: Mar. 16, 2017;
Published: Apr. 11, 2017
Views 1640 Downloads 67
Mahmoud M. El-borai, Faculty of Science, Alexandria University, Alexandria, Egypt
Wagdy G. ElSayed, Faculty of Science, Alexandria University, Alexandria, Egypt
M. A. Abdou, Faculty of Education, Alexandria University, Alexandria, Egypt
M. Taha E., Faculty of Education, Alexandria University, Alexandria, Egypt
We present a necessary optimality conditions for a class of optimal control problems. The dynamical control system involves integer and fractional order derivatives and the final time is free. Optimality conditions are obtained. Feedback control laws for linear dynamic system are obtained.
Mahmoud M. El-borai,
Wagdy G. ElSayed,
M. A. Abdou,
M. Taha E.,
On The Fractional Optimal Control Problem with Free End Point, American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics.
Vol. 6, No. 5-1,
2017, pp. 46-50.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A. Debbouche and M. M. El-Borai, "Weak almost periodic and optimal mild solutions of fractional evolution equations". Electronic Journal of Differential Equations, vol. 2009, pp. 1-8, (2009).
Mahmoud M. El-Borai, "Some probability densities and fundamental solutions of fractional evolution equations". Chaos, Solitons & Fractals, vol. 14, pp. 433-440, (2002).
Mahmoud. M. El-Borai, Khairia El-Said El-Nadi, and E. G. El-Akabawy, "On some fractional evolution equations". Computers and mathematics with applications, vol. 59, pp. 1352-1355, (2010).
O. P. Agrawal, A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dynam. 38 (2004), no. 1-4, 323-337.
Mahmoud M. El-Borai, W. G. Elsayed and F. N. Ghaffoori, On the Cauchy Problem for Some Parabolic Fractional Partial Differential Equations with Time Delays, J. Math. & System Scie. 6 (2016), 194-199.
Mahmoud M. El-Borai, W. G. Elsayed and R. M. Al-Masroub, Exact Solutions for Some Nonlinear Partial Differential Equations via Extended (G'/G) – Expansion Method, Inter. J. Math. Trends and Tech. (IJMTT) – Vol. 36, No. 1-Aug (2016), 60-71.
O. P. Agrawal, A formulation and numerical scheme for fractional optimal control problems. J. Vib. Control 14 (2008), no. 9-10, 1291-1299.
O. P. Agrawal, O. Defterli and D. Baleanu, Dumitru Fractional optimal control problems with several state and control variables. J. Vib. Control 16 (2010), no. 13, 1967-1976.
G. S. F. Frederico and D. F. M. Torres, Fractional optimal control in the sense of Coputo and the fractional Noether’s theorem. Int. Math. Forum 3 (2008), no. 9-12, 479-493.
G. S. F. Frederico and D. F. M. Torres. Fractional conservation laws in optimal control theory, Nonlinear Dynam. 53 (2008), no. 3, 215-222.
C. Tricaud and Y. Chen. An approximate method for numerically solving fractional order optimal control problems of general form. Comput. Math. Appl. 59 (2010), no. 5, 1644-1655.
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier, North-Holland Mathematics Studies, (2006), p: 204.
S. G. Samko, A. A. Kibas O. I. Marichev. Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, (2004).
C. Tricaud and Y. Chen. Time Optimal Control of Systems with Fractional Dynamics, Int. J. Differ. Equ. Appl., Volume 2010 (2010). Article ID 461048.
Z. D. Jelicic and N. Petrovacki, Optimality conditions and a solution scheme for fractional optimal control problems, Struct. Multidiscipline. Optimum. 38 (2009), no. 6, 571–581.
Mahmoud M. El-Borai, Khairia El-Said El-Nadi, On the fractional optimal control, Int. J. of Appl. Math. and Mech. (2008), 13-18.
Pontryagin LS, Baltyanskii VG, Gamkrelidze RV, and Mischenko EF (1962). The mathematical theory of optimal process. Inter science publishers Inc, New York.