Abstract
Over the past few decades, significant medical advances have been made in the area of drug delivery with the development of controlled release dosage forms. Controlled release formulations bring scientists in different fields to work together with the common aim of realizing more and more effective products. For this purpose, the use of mathematical modeling turns out to be very useful as this approach enables, in the best case, the prediction of release kinetics before the release systems are realized. In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving initial-boundary value problem describing the Fick’s second law
Keywords
Controlled drug release Fick’s second law fractional differential equation collocation method
References
- Gülsu M., Öztürk Y., Sezer M. 2011. Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid, J. Avdan. Research Diff. Equa., 3 (4): 1-13.
- Gülsu M.,Öztürk Y.,Anapalı A. 2013. Numerical approach for solving fractional
- relaxation-oscillation equation, Appl.Math.Modelling, 37(8):5927-5937.
- Gülsu M., Öztürk Y., Sezer M. 2012. A New Chebyshev Polynomial Approximation for Solving Delay Differential Equations, J. Diff. Equa. Appl., 18 (6) :1043-1065.
- Gülsu M., Öztürk Y., Sezer M. 2012. Numerical Approach for Solving Volterra Integro
- Differential Equations with Piecewise Intervals, J. Avdan. Research Appl. Math. 4 (1):23-37.
- Odibat Z., Shawagfeh N. T. 2007. Generalized Taylor’s Formula, Appl. Math. Comp., 186(1):286–293.
- Podlubny I. 1999. Fractional Differential Equations, Academic Press, New York.
- He J. H. 1998. Nonlinear Oscillation with Fractional Derivative and its Applications, International Conference on Vibrating Engineering, Dalian, China.
- He J. H. 1999. Some Applications of Nonlinear Fractional Differential Equations and Their Approximations, Bull. Sci. Technol., 15(2):86–90.
- Ahmad W. M., El-Khazali R. 2007. Fractional-Order Dynamical Models of Love, Chaos, Solitons & Fractals, 33:1367-1375.
- Lewandowski R., Chorazyczewski B. 2010. Identification of the Parameters of the Kelvin–Voigt and the Maxwell Fractional Models, Used to Modeling of Viscoelastic Dampers, Comput. Struct., 88:1–17.
- Bagley R. L., Torvik P. J. 1984. On the Appearance of the Fractional Derivative in the Behavior of Real Materials, J. Appl. Mech., 51:294–298.
- Bagley R. L., Torvik P. J. 1985. Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures, AIAA J., 23(6):918–925.
- Glockle W. G., Nonnenmacher T. F. 1995. A Fractional Calculus Approach to Self-Similar Protein Dynamics, Biophys. J., 68:46–53.
- Magin R. L. 2006. Fractional calculus in bioengineering, Begell House Publishers.
- Daşçıoğlu A. Yaslan H. 2011. The Solution of High-Order Nonlinear Ordinary Differential
- Equations by Chebyshev Polynomials, Appl. Math. Comput., 217(2):5658-5666.
Abstract
Son birkaç yıldır kontollü ilaç salım dozaj formlarındaki gelişmeler ile birlikte, ilaç salım alanında önemli
medikal ilerlemeler sağlanmıştır. Kontrollü ilaç salım formülasyonları, daha da etkili ürünler geliştirmek
amacıyla çeşitli alanlardaki bilim adamlarını birlikte çalışmak üzere biraraya getirmiştir. Bu amaçla, bu
yaklaşım, matematiksel modelleme kullanımının önemini ortaya koymakta daha da önemlisi, salım sistemleri
gerçekleştirilmeden önce salım kinetiği tahmini yapılabilmektedir. Bu çalışmada ikinci Fick kanununu
tanımlayan başlangıç sınır değer probleminin nümerik çözümü için sıralama yöntemini temel alan Taylor
sıralama yöntemi verilmiştir.
Keywords
Kontrollü ilaç salımı İkinci Fick kanunu kesirli türevli diferansiyel denklem sıralama yöntemi
References
- Gülsu M., Öztürk Y., Sezer M. 2011. Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid, J. Avdan. Research Diff. Equa., 3 (4): 1-13.
- Gülsu M.,Öztürk Y.,Anapalı A. 2013. Numerical approach for solving fractional
- relaxation-oscillation equation, Appl.Math.Modelling, 37(8):5927-5937.
- Gülsu M., Öztürk Y., Sezer M. 2012. A New Chebyshev Polynomial Approximation for Solving Delay Differential Equations, J. Diff. Equa. Appl., 18 (6) :1043-1065.
- Gülsu M., Öztürk Y., Sezer M. 2012. Numerical Approach for Solving Volterra Integro
- Differential Equations with Piecewise Intervals, J. Avdan. Research Appl. Math. 4 (1):23-37.
- Odibat Z., Shawagfeh N. T. 2007. Generalized Taylor’s Formula, Appl. Math. Comp., 186(1):286–293.
- Podlubny I. 1999. Fractional Differential Equations, Academic Press, New York.
- He J. H. 1998. Nonlinear Oscillation with Fractional Derivative and its Applications, International Conference on Vibrating Engineering, Dalian, China.
- He J. H. 1999. Some Applications of Nonlinear Fractional Differential Equations and Their Approximations, Bull. Sci. Technol., 15(2):86–90.
- Ahmad W. M., El-Khazali R. 2007. Fractional-Order Dynamical Models of Love, Chaos, Solitons & Fractals, 33:1367-1375.
- Lewandowski R., Chorazyczewski B. 2010. Identification of the Parameters of the Kelvin–Voigt and the Maxwell Fractional Models, Used to Modeling of Viscoelastic Dampers, Comput. Struct., 88:1–17.
- Bagley R. L., Torvik P. J. 1984. On the Appearance of the Fractional Derivative in the Behavior of Real Materials, J. Appl. Mech., 51:294–298.
- Bagley R. L., Torvik P. J. 1985. Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures, AIAA J., 23(6):918–925.
- Glockle W. G., Nonnenmacher T. F. 1995. A Fractional Calculus Approach to Self-Similar Protein Dynamics, Biophys. J., 68:46–53.
- Magin R. L. 2006. Fractional calculus in bioengineering, Begell House Publishers.
- Daşçıoğlu A. Yaslan H. 2011. The Solution of High-Order Nonlinear Ordinary Differential
- Equations by Chebyshev Polynomials, Appl. Math. Comput., 217(2):5658-5666.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 1, 2013 |
| Submission Date | January 5, 2015 |
| Published in Issue | Year 2013 Volume: 2 Issue: 2 |