THERMAL SCIENCE

International Scientific Journal

Ahmad Haghbin

,

Hossein Jafari

,

Pranay Goswami

,

Vernon Morganathan Ariyan

SOLVING TIME-FRACTIONAL CHEMICAL ENGINEERING EQUATIONS BY GENERALIZED DIFFERENTIAL TRANSFORM METHOD

ABSTRACT
In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.
KEYWORDS
fractional differential equations, differential transform method, chemical reactor, reaction, concentration
PAPER SUBMITTED: 2020-04-20
PAPER REVISED: 2020-05-30
PAPER ACCEPTED: 2020-06-10
PUBLISHED ONLINE: 2020-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI20S1157H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Supplement 1, PAGES [S157 - S164]
REFERENCES
  1. Baleanu, D., et al., Fractional Calculus: Models and Numerical Methods, World Scientific, Singapore, 2012
  2. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006, Vol. 204
  3. Kiryakova, V., Generalized Fractional Calculus and Applications, Longman and J. Wiley, Harlow-New York, USA, 1994
  4. Jafari, H., Tajadodi, H., New Method for Solving a Class of Fractional Partial Differential Equations with Applications, Thermal Science, 22 (2018), Suppl. 1, pp. S277-S286
  5. Moallem, G. R., et al., A Numerical Scheme to Solve Variable Order Diffusion-Wave Equations, Thermal Science, 23 (2019), Suppl. 6, pp. S2063-S2071
  6. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, Cal., USA, 1999
  7. Samko, S. G., et al., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993
  8. Zhou, J. K., Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 2006
  9. Arikoglu, A., Ozkol, I., Solution of Fractional Differential Equations by Using Differential Transform Method, Chaos Soliton Fract., 34 (2007), 5, pp. 1473-1481
  10. Erturk, V. S., et al., Application of Generalized Differential Transform Method to Multi-Order Fractional Differential Equations, Commun. Non-linear Sci. Numer. Simul., 13 (2008), 8, pp. 1642-1654
  11. Odibat, Z., Shawagfeh, N., Generalized Taylor's Formula, Appl Math Comput., 186 (2007), 1, pp. 286-293
  12. Arikoglu, A., Ozkol, I., Comments on Application of Generalized Differential Transform Method to Multi-Order Fractional Differential Equations, Erturk, V. S., et al.,
  13. Al-Mdallal, Q. M., An Efficient Method for Solving Fractional Sturm-Liouville Problems, Chaos Solitons and Fractals, 40 (2009), 1, pp. 183-189
  14. Al-Mdallal, Q. M., On the Numerical Solution of Fractional Sturm-Liouville Problems, International Journal of Computer Mathematics, 87 (2010), 12, pp.2837-2845
  15. Al-Rabtah, A., et al., Solutions of a Fractional Oscillator by Using Differential Transform Method, Computers and Mathematics with Applications, 59 (2010), 3, pp. 1356-1362
  16. Gupta, P. K., Approximate Analytical Solutions of Fractional Benney-Lin Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method, Computers and Mathematics with Applications, 61 (2011), 9, pp. 2829-2842
  17. Kurulay, M., Bayram M., Approximate Analytical Solution for the Fractional Modified KdV by Differential Transform Method, Commun. Non-linear Sci. Numer. Simul., 15 (2010), 7, pp. 1777-1782
  18. Nazari, D., Shahmorad, S., Application of the Fractional Differential Transform Method to Fractional-Order Integro-Differential Equations with Non-Local Boundary Conditions, Journal Comput. Appl. Math., 234 (2010), 3, pp. 883-891
  19. Erturk, V. S., Momani, S., Solving Systems of Fractional Differential Equations Using Differential Transform Method, Journal of Computational and Applied Mathematics, 215 (2008), 1, pp. 142-151
  20. Arkoglu, A., Ozkol, I., Solution of Fractional Integro-Differential Equations by Using Fractional Differential Transform Method, Chaos, Solitons and Fractals, 40 (2009), 2, pp. 521-529
  21. Nazari, D., Shahmorad, S., Application of Fractional Differential Transform Method to the Fractional Order Integro-Differential Equations with Non-Local Boundary Conditions, Journal of Computational and Applied Mathematics, 234 (2010), pp. 3, 883-891
  22. Inc, M., Ugurlu, Y., Numerical Simulation of the Regularized Long Wave Equation by He's Homotopy Perturbation Method, Physics Letters A, 369 (2007), 3, pp. 173-179
  23. Inc, M., The Approximate and Exact Solutions of the Space- and Time-Fractional Burgers Equations with Initial Conditions by Variational Iteration Method, Journal Math. Analysis Applic., 345 (2008), 1, pp. 476-484
  24. Haghbin, A., Jafari, H., Solving Time-Fractional Chemical Engineering Equations by Modified Variational Iteration Method as Fixed Point Iteration Method, Iranian Journal of Mathematical Chemistry, 8 (2017), 4, pp. 365-375
  25. Jang, B., Efficient Analytic Method for Solving Non-Linear Fractional Differential Equations, Applied Mathematical Modelling, 38 (2014), 5-6, pp. 1775-1787
  26. Odibat, Z., et al., Generalized Differential Transform Method: Application Differential Equations of Fractional Order, Appl. Math. Comput., 197 (2008), 2, pp. 467-477
PDF VERSION [DOWNLOAD]
Solving time-fractional chemical engineering equations by generalized differential transform method

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence