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New and Extended Applications of the Natural and Sumudu Transforms: Fractional Diffusion and Stokes Fluid Flow Realms

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Advances in Real and Complex Analysis with Applications

Part of the book series: Trends in Mathematics ((TM))

Abstract

The Natural transform is used to solve fractional differential equations for various values of fractional degrees \(\alpha \), and various boundary conditions. Fractional diffusion problems solutions are analyzed, followed by Stokes–Ekman boundary thickness problem. Furthermore, the Sumudu transform is applied for fluid flow problems, such as Stokes, Rayleigh, and Blasius, toward obtaining their solutions and corresponding boundary layer thickness.

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References

  1. Z.H. Khan, W.A. Khan, N-transform properties and applications. NUST J. Eng. Sci. 1(1), 127–133 (2008)

    Google Scholar 

  2. R. Silambarasan, F.B.M. Belgacem, Applications of the natural transform to Maxwell’s equations, in PIERS Proceedings in Suzhou, China. Sept 12–16 (2011), pp 899–902

    Google Scholar 

  3. F.B.M. Belgacem, R. Silambarasan, Theory of natural transform. Int. J. Math. Eng. Sci. Aeorosp. (MESA) 3(1), 99–124 (2012)

    MATH  Google Scholar 

  4. F.B.M. Belgacem, R. Silambarasan, Maxwell’s equations solutions by means of the Natural transform. Spec. Iss. Complex Dyn. Syst. Nonlinear Methods Math. Models Thermodyn. Int. J. Math. Eng. Sci. Aerosp. (MESA), 3(3), 313–323 (2012)

    Google Scholar 

  5. F.B.M. Belgacem, R. Silambarasan, The Generalized nth order Maxwell’s equations, in PIERS Proceedings Held in Moscow Technical University of Radio Engineering, Electronics and Automatics (MIREA) (Moscow, Russia, 2012), pp 500–503

    Google Scholar 

  6. F.B.M. Belgacem, R. Silambarasan, Advances in the natural transform. AIP Conf. Proc. 1493(1), 106–110 (2012)

    Article  Google Scholar 

  7. D. Loonker, P.K. Banerji, Solution of fractional ordinary differential equations by natural transform. Int. J. Math. Eng. Sci. 2(12), 1–7 (2013)

    MATH  Google Scholar 

  8. D. Loonker, P.K. Banerji, Natural transform for distribution and Boehmian spaces. Math. Eng. Sci. Aerosp. 4(1), 69–76 (2013)

    MATH  Google Scholar 

  9. S.K.Q. Al-Omari, On the applications of natural transform. Int. J. Pure Appl. Math. 85(4), 729–744 (2013)

    Article  Google Scholar 

  10. D. Loonker, P.K. Banerji, Natural transform and solution of integral equations for distribution spaces. American. J. Math. Sci. 3(1), 65–72 (2014)

    Google Scholar 

  11. S. Maitama, A new approach to linear and nonlinear Schr\(\ddot{o}\)dinger equations using the natural decomposition method. Int. Math. Forum 9(17), 835–847 (2014)

    Article  Google Scholar 

  12. S.K.Q. Al-Omari, On some q-analogues of the natural transform and further investigations, arXiv:1505.02179v1 [math.CA] (2015), pp. 1–16

  13. D. Poltem, P. Totassa, A. Wiwatwanich, Application of decomposition method for natural transform. Asian. J. of Appl. Sci. 3(6), 905–909 (2015)

    Google Scholar 

  14. K. Shah, M. Junaid, N. Ali, Extraction of laplace, Sumudu, fourier and Mellin transform from the natural transform. J. Appl. Environ. Biol. Sci. 5(9), 108–115 (2015)

    Google Scholar 

  15. A.S. Abdel-Rady, S.Z. Rida, A.A.M. Arafa, H.R. Abedl-Rahim, Natural transform for solving fractional models. J. Appl. Math. Phys. 3, 1633–1644 (2015)

    Article  Google Scholar 

  16. M. Junaid, Application of natural transform to Newtonian fluid problems. Eur. Int. J. Sci. Technol. 5(4), 138–147 (2016)

    Google Scholar 

  17. S. Maitama, A hybrid Natural transform Homotopy perturbation method for solving fractional partial differential equations. Int. J. Differ. Equ. 2016, 1–7 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Omran, A. Kiliman, Natural transform of fractional order and some properties, in Cogent Mathematics (2016), pp. 1–8

    Google Scholar 

  19. S. Maitama, A new analytical approach to linear and nonlinear partial differential equations. Nonlinear Stud. 23(4), 675–684 (2016)

    MathSciNet  MATH  Google Scholar 

  20. S. Maitama, Explicit solution of solitary wave equation with compact support by natural homotopy perturbation method. Math. Eng. Sci. Aerosp. 7(4), 625–635 (2016)

    MathSciNet  Google Scholar 

  21. F.B.M. Belgacem, A.A. Karaballi, S.L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations. Math. Probl. Eng. (MPE) 3, 103–118 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. F.B.M. Belgacem, A.A. Karaballi, Sumudu transform fundamental properties investigations and applications. J. Appl. Math. Stoch. Anal. (JAMSA) 91083, 1–23 (2005)

    Google Scholar 

  23. F.B.M. Belgacem, Introducing and analysing deeper Sumudu properties. Nonlinear Stud. J. (NSJ) 13(1), 23–41 (2006)

    MathSciNet  MATH  Google Scholar 

  24. M.G.M. Hussain, F.B.M. Belgacem, Transient solutions of Maxwell’s equations based on Sumudu transform. Progr. Electromagn. Res. 74, 273–289 (2007)

    Article  Google Scholar 

  25. F.B.M. Belgacem, Sumudu transform applications to Bessel’s functions and equations. Appl. Math. Sci. 4(74), 3665–3686 (2010)

    MathSciNet  MATH  Google Scholar 

  26. Q.K. Katatbeh, F.B.M. Belgacem, Applications of the Sumudu transform to fractional differential equations. Nonlinear Stud. (NSJ) 18(1), 99–112 (2011)

    Google Scholar 

  27. P. Goswami, F.B.M. Belgacem, Fractional differential equations solutions through a Sumudu rational. Nonlinear Stud. J. (NSJ) 19(4), 591–598 (2012)

    Google Scholar 

  28. F.B.M. Belgacem, R. Silambarasan, Laplace transform analytical restructure. Appl. Math. (AM) 4, 919–932 (2013)

    Article  Google Scholar 

  29. H. Bulut, H.M. Baskonus, F.B.M. Belgacem, The analytical solution of some fractional ordinary differential equations by the Sumudu transform method. J. Abstr. Appl. Anal. Article ID 203875, 1–6 (2013)

    Google Scholar 

  30. Z. Hammouch, T. Mekkaoui, F.B.M. Belgacem, Numerical simulations for a variable order fractional Schnakenberg model. AIP Conf. Proc. 1637, 1450–1455 (2014)

    Article  Google Scholar 

  31. S.T. Demiray, H. Bulut, F.B.M. Belgacem, Sumudu transform method for analytical solutions of fractional type ordinary differential equations. J. Math. Probl. Eng. (2014)

    Google Scholar 

  32. D.S. Tuluce, H. Bulut, F.B.M. Belgacem, Sumudu transform method for analytical solutions of fractional type ordinary differential equations. Math. Probl. Eng. Spec. Iss. Par. Fract. Equ. Appl. 1–6 (2014)

    Google Scholar 

  33. T. Mekkaoui, H. Zakia, F.B.M. Belgacem, A. El Abbassi, Fractional-order nonlinear systems: chaotic dynamics, numerical simulation and circuits design, chapter, in Fractional Dynamics (2015), pp. 343–356

    Google Scholar 

  34. F.B.M. Belgacem, V. Gulati, P. Goswami, A. Aljouiee, On generalized fractional differential equations solutions: Sumudu transform solutions and applications, Chap. 22 in De Gruyter open, in Fractional Dynamics (2015), pp. 382–393

    Google Scholar 

  35. H. Zakia, T. Mekkaoui, F.B.M. Belgacem, Double-diffusive natural convection in porous cavity heated by an internal boundary. Math. Eng. Sci. Aerosp. 7(3), 453–466 (2016)

    Google Scholar 

  36. F.B.M. Belgacem, C. Cattani, Sumudu transform of Weierstrass functions, in CMES Conference (2016)

    Google Scholar 

  37. F.B.M. Belgacem, R. Silambarasan, Further distinctive investigations of the Sumudu transform, in Submitted to ICNPAA Conference, France, and Accepted in AIP Conferences Proceedings (2016)

    Google Scholar 

  38. F.B.M. Belgacem, R. Silambarasan, Sumudu transform of Dumont bimodular Jacobi elliptic functions for arbitrary powers, in Submitted to ICNPAA Conference, France, and Accepted in AIP Conferences Proceedings (2016)

    Google Scholar 

  39. F.B.M. Belgacem, R. Silambarasan, A distinctive Sumudu treatment of trigonometric functions. J. Comput. Appl. Math. 312, 74–81 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  40. F.B.M. Belgacem, E.H. Al-Shemas, R. Silambarasan, Sumudu computation of the transient magnetic field in a lossy medium. Appl. Math. Inf. Sci. 11(1), 209–217 (2017)

    Article  Google Scholar 

  41. A. Erd\(\acute{e}\)lyi, Tables of Integral Transforms, vol. 1 (McGraw-Hill Inc., 1954)

    Google Scholar 

  42. T. Myint-U, L. Debnath, Linear Partial Differential Equations for Scientists and Engineers (Birkhäuser Inc., Boston, 2007)

    MATH  Google Scholar 

  43. L. Debnath, D. Bhatta, Integral Transforms and their Applications (Chapman & Hall/CRC, Boca Raton, 2007)

    MATH  Google Scholar 

  44. L. Bernardin et al., Maple Programming Guide (Waterloo Maple Inc., 2011)

    Google Scholar 

  45. F.B.M. Belgacem, Sumudu applications to Maxwell’s equations. PIERS Online 5(4), 355–360 (2009)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Basic Education, Department of Mathematics, PAAET, Al-ardhiya, Kuwait

    Fethi Bin Muhammed Belgacem

  2. IT Networking, Department of Information Technology, SITE, VIT University, Vellore, Tamilnadu, India

    Rathinavel Silambarasan

  3. E3MI Group, Faculty of Sciences and Techniques of Errachidia, Department of Mathematics, Moulay Ismail University, 52000, Meknes, Morocco

    Hammouch Zakia & Toufik Mekkaoui

Authors
  1. Fethi Bin Muhammed Belgacem
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  2. Rathinavel Silambarasan
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  3. Hammouch Zakia
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  4. Toufik Mekkaoui
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Corresponding author

Correspondence to Fethi Bin Muhammed Belgacem .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

  2. Department of Mathematics Education and the RINS, Gyeonsang National University, Jinju, Korea (Republic of)

    Yeol Je Cho

  3. Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  4. Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo, Universidade de Vigo, Ourense, Spain

    Iván Area

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Belgacem, F.B.M., Silambarasan, R., Zakia, H., Mekkaoui, T. (2017). New and Extended Applications of the Natural and Sumudu Transforms: Fractional Diffusion and Stokes Fluid Flow Realms. In: Ruzhansky, M., Cho, Y., Agarwal, P., Area, I. (eds) Advances in Real and Complex Analysis with Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-10-4337-6_6

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