Correction to: Analytical approximate solutions of the fractional convection–diffusion equation with nonlinear source term by He's homotopy perturbation method (International Journal of Computer Mathematics, (2010), 87, 5, (1057-1065), 10.1080/00207160903023581);Analytical approximate solutions of the fractional convection-diffusion equation with nonlinear source term by He's homotopy perturbation method

International Journal of Computer Mathematics

Volumn 87, Issue 5, 2010, Pages 1057-1065

  Momani, Shaher ^a   Yildirim, Ahmet ^b  

^a MUTAH UNIVERSITY   (Jordan)

^b EGE UNIVERSITY   (Turkey)

Author keywords

Caputo fractional derivative; Convection diffusion equation; Fractional differential equations; Homotopy perturbation method

Indexed keywords

DIFFERENTIATION (CALCULUS); DIFFUSION IN LIQUIDS; HEAT CONVECTION; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

ANALYTICAL APPROXIMATE SOLUTION; CAPUTO FRACTIONAL DERIVATIVES; CONVECTION-DIFFUSION EQUATIONS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; HE'S HOMOTOPY PERTURBATION METHODS; HOMOTOPY PERTURBATION METHOD (HPM); NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 77952597982     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160.2021.1908711     Document Type: Erratum

References (40)

1. S. Das, Solution of fractional vibration equation by the variational iteration method and modified decomposition method, Int. J. Nonlinear Sci. Numer. Simul. 9 (2008), p. 361.
2. M. Dehghan and F. Shakeri, Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method, Phys. Scripta 75 (2007), p. 778.
3. M. Dehghan and F. Shakeri, Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method, Prog. Electromagn. Res. PIER 78 (2008), p. 361.
4. M. Dehghan and F. Shakeri, Use of He's homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, J. Porous Media 11 (2008), p. 765.
5. M. Dehghan and A. Shokri, A numerical method for solving the hyperbolic telegraph equation, Numer. Methods Partial Differential Equations 24 (2008), p. 1080.
6. Z.Z. Ganji, D.D. Ganji, H. Jafari and M. Rostamian, Application of the homotopy perturbation method to coupled system of partial differential equations with time fractional derivatives, Topol. Methods Nonlinear Anal. 31 (2008), p. 341.
7. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg. 167(1998), p. 57.
8. J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg. 178 (1999), p. 257.
9. J.H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput. 151 (2004), p. 287.
10. J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals 26 (2005), pp. 695-700.
11. J.H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul. 6 (2005), p. 207.
12. J.H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett. A 350 (2006), p. 87.
13. J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Modern Phys. B 20 (2006), p. 1141.
14. J.H. He, New interpretation of homotopy perturbation method, Int. J. Modern Phys. B 20 (2006), p. 2561.
15. J.H. He, Recent development of the homotopy perturbation method, Topol. Methods Nonlinear Anal. 31 (2008), p. 205.
16. J.H. He, An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Modern Phys. B 22 (2008), p. 3487.
17. Y. Luchko and R. Gorneflo, The initial value problem for some fractional differential equations with the Caputo derivative, preprint series A08-98, Fachbreich Mathematik und Informatik, Freic Universitat Berlin, 1998.
18. F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F Mainardi, eds., Springer-Verlag, New York, 1997.
19. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
20. α(x), Rend. Accad. Lincei (Ser. V) 13 (1904), p. 3.
21. S. Momani, An algorithm for solving the fractional convection-diffusion equation with nonlinear source term, Commun. Nonlinear. Sci. Numer. Simul. 12 (2007), p. 1283.
22. S. Momani and Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A 365 (2007), p. 345.
23. S. Momani, Z. Odibat, and I. Hashim, Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods, Topol. Methods Nonlinear Anal. 31 (2008), p. 211.
24. Z. Odibat and S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul. 7 (2006), p. 27.
25. Z. Odibat and S. Momani, Applications of variational iteration and homotopy perturbation methods to fractional evolution equations, Topol. Methods Nonlinear Anal. 31 (2008), p. 227.
26. K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
27. G. Oturanc, A. Kurnaz, and Y. Keskin, A new analytical approximate method for the solution of fractional differential equations, Int. J. Comput. Math. 85 (2008), p. 131.
28. T. Öziş and A. Yildirim, A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities, Int. J. Nonlinear Sci. Numer. Simul. 8 (2007), p. 243.
29. T. Öziş and A. Yildirim, Traveling wave solution of Korteweg-de Vries Equation using He's homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul. 8 (2007), p. 239.
30. I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
31. A. Saadatmandi, M. Dehghan, and A. Eftekhari, Application of He's homotopy perturbation method for nonlinear system of second-order boundary value problems, in Nonlinear Analysis: Real World Applications, 10(3) (2009), p. 1912.
32. S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993.
33. F. Shakeri and M. Dehghan, Inverse problem of diffusion equation by He's homotopy perturbation method, Phys. Scripta 75 (2007), p. 551.
34. F. Shakeri and M. Dehghan, Solution of the delay differential equations via homotopy perturbation method, Math. Comput. Model. 48 (2008), p. 486.
35. R.F. Sincovec and N.K. Madsen, Software for non-linear partial differential equations, ACM Trans. Math. Software (1975).
36. A. Yildirim, Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method, Comput. Math. Appl. 56 (2008), p. 3175.
37. A. Yildirim, The homotopy perturbation method for approximate solution of the modified KdV equation, Z. Naturforsch. 63a (2008), p. 621.
38. A. Yildirim, He's homotopy perturbation method for nonlinear differential-difference equations, Int. J. Comput. Math. 87 (2010), pp. 992-996.
39. A. Yildirim, Application of the homotopy perturbation method for the Fokker-Planck equation, Commun. Numer. Methods Engrg., in press, DOI:10.1002/cnm.1200.
40. A. Yildirim and T. Öziş, Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method, Phys. Lett. A 369 (2007), p. 70.