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A Hybrid Computational Scheme for Solving Local Fractional Partial Differential Equations

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Advances in Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 953))

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Abstract

A new type of methodology termed the local fractional natural homotopy perturbation method (LFNHPM) with the local fractional derivative operator (LFDO) was implemented in this study. The hybrid methodology combines the natural transform method (NTM) with the homotopy perturbation method (HPM).To validate and illustrate the efficacy of the current method, two challenges are solved. The results obtained using the LFNHPM show excellent agreement with the LFVIM and LFRDTM, demonstrating that the LFNHPM is an effective approach for obtaining the approximate and closed-form solutions of fractional models. We established that our approach for fractional models is accurate and straightforward and researcher can use this approach to solve various problems.

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References

  1. Podlubny, I.: Fractional differential equations. In: Mathematics in Science and Engineering, Academic Press, New York (1999)

    Google Scholar 

  2. Srivastava, H.M., Jena, R.M., Chakraverty, S., Jena, S.K.: Dynamic response analysis of fractionally-damped generalized Bagley-Torvik equation subject to external loads. Russ. J. Math. Phys. 27, 254–268 (2020)

    Article  MathSciNet  Google Scholar 

  3. Mahto, L., Abbas, S., Hafayed, M., Srivastava, H.M.: Approximate controllability of sub diffusion equation with impulsive condition. Mathematics 7(2), 190 (2019)

    Article  Google Scholar 

  4. Wang, S.Q., Yang, Y.J.: Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative. Abstr. Appl. Anal. 2014, 1–7 (2014)

    MathSciNet  Google Scholar 

  5. Jassim, H.K., Ünlü, C., Moshokoa, S.P., Khalique, C.M.: Local fractional laplace variational iteration method for solving diffusion and wave equations on cantor sets within local fractional operators. Math. Probl. Eng. 2015, 1–9 (2015)

    Article  MathSciNet  Google Scholar 

  6. Mohsin, N.H., Jassim, H.K., Azeez, A.D.: A New analytical method for solving nonlinear burger’s and coupled burger’s equations. Mater. Today: Proc. 80(3), 3193–3195 (2023)

    Google Scholar 

  7. Jafari, H., Jassim, H.K., Moshokoa, S.P., Ariyan, V.M., Tchier, F.: Reduced differential transform method for partial differential equations within local fractional derivative operator. Adv. Mech. Eng. 8(4), 1–6 (2016)

    Article  Google Scholar 

  8. Jassim, H.K., Hussein, M.A.: A new approach for solving nonlinear fractional ordinary differential equations. Mathematics 11(7), 1565 (2023)

    Article  Google Scholar 

  9. Ziane, D., Cherif, M.H., Belghaba, K., Jassim, H.K., Al-Dmour, A.: Application of local fractional variational iteration transform method to solve nonlinear wave-like equations within local fractional derivative. Progr. Fract. Different. Appl. 9(2), 311–318 (2023)

    Article  Google Scholar 

  10. Singh, J., Jassim, H.K., Kumar, D.: An efficient computational technique for local fractional Fokker-Planck equation. Physica A 555(124525), 1–8 (2020)

    MathSciNet  Google Scholar 

  11. Jassim, H.K.: Solving poisson equation within local fractional derivative operators. Res. Appl. Math. 1, 1–12 (2017)

    Google Scholar 

  12. Jassim, H.K.: Extending application of adomian decomposition method for solving a class of volterra integro-differential equations within local fractional integral operators. J. Coll. Educ. Pure Sci. 7(1), 19–29 (2017)

    Google Scholar 

  13. Yang, X.J.: Advanced Local Fractional Calculus and its Applications. World Science Publisher, New York (2012)

    Google Scholar 

  14. Yang, X.J.: Local Fractional Functional Analysis and its Applications. Asian Academic Publisher Limited, Hong Kong (2011)

    Google Scholar 

  15. Maitama, S.: Local fractional natural homotopy perturbation method for solving partial differential equations with local fractional derivative. Progr. Fract. Different. Appl. 4, 219–228 (2018)

    Article  Google Scholar 

  16. Chen, L.: Local fractional variational iteration method for local fractional poisson equations in two independent variables. Abstr. Appl. Anal. 2014, 1–7 (2014)

    MathSciNet  Google Scholar 

  17. Gómez-Aguilar, J.F., et al.: Analytical solutions of the electrical RLC circuit via liouville-caputo operators with local and non-local kernels. Entropy 18, 1–12 (2016)

    Article  Google Scholar 

  18. Ziane, D., Cherif, M.H.: Variational iteration transform method for fractional differential equations. J. Interdisc. Math. 21(1), 185–199 (2018)

    Article  Google Scholar 

  19. Hussein, M.A.: Approximate methods for solving fractional differential equations. J. Educ. Pure Sci.-Univ. Thi-Qar 12(2), 32–40 (2022)

    Google Scholar 

  20. Jafari, H., Zayir, M.Y., Jassim, H.K.: Analysis of fractional Navier-Stokes equations. Heat Transfer 52(3), 2859–2877 (2023)

    Article  Google Scholar 

  21. Baleanu, D., Jassim, H.K., Al Qurashi, M.: Solving helmholtz equation with local fractional derivative operators. Fractal Fract. 3(43), 1–13 (2019)

    Google Scholar 

  22. Baleanu, D., Jassim, H.K.: Exact solution of two-dimensional fractional partial differential equations. Fractal Fract. 4(21), 1–9 (2020)

    Google Scholar 

  23. Khafif, S.A.: SVIM for solving Burger’s and coupled Burger’s equations of fractional order. Progr. Fract. Different. Appl. 7(1), 1–6 (2021)

    Google Scholar 

  24. Kumar, D., Jassim, H.K., Singh, J., Dubey,: A computational study of local fractional helmholtz and coupled helmholtz equations in fractal media. In: Lecture Notes in Networks and Systems, LNNS, vol. 666, pp. 286–298 (2023). https://doi.org/10.1007/978-3-031-29959-9_18

  25. Hussein, M.A., Jassim, H.K.: Analysis of fractional differential equations with Antagana-Baleanu fractional operator. Progr. Fract. Different. Appl. 9(4), 681–686 (2023)

    Article  Google Scholar 

  26. Mahdi, S.H., Jassim, H.K.: A new technique of using Adomian decomposition method for fractional order nonlinear differential equations. AIP Conf. Proc. 2414(040075), 1–12 (2023)

    Google Scholar 

  27. Mahdi, S.H., Jassim, H.K., Hassan, N.J.: A new analytical method for solving nonlinear biological population model. AIP Conf. Proc. 2398(060043), 1–12 (2022)

    Google Scholar 

  28. Zayir, M.Y., Jassim, H.K.: A unique approach for solving the fractional Navier-Stokes equation. J. Multiplicity Math. 25(8-B), 2611–2616 (2022)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, 302004, India

    Devendra Kumar

  2. Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq

    Hassan Kamil Jassim & Mohammed Diykh

  3. College of Technical Engineering, National University of Science and Technology, Thi-Qar, Iraq

    Hassan Kamil Jassim

  4. Department of Mathematics, JECRC University, Jaipur, Rajasthan, 303905, India

    Jagdev Singh

Authors
  1. Devendra Kumar
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  2. Hassan Kamil Jassim
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  3. Jagdev Singh
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  4. Mohammed Diykh
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Corresponding author

Correspondence to Jagdev Singh .

Editor information

Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, India

    Jagdev Singh

  2. Department of Mathematics, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  3. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Dumitru Baleanu

  4. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India

    Devendra Kumar

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Kumar, D., Jassim, H.K., Singh, J., Diykh, M. (2024). A Hybrid Computational Scheme for Solving Local Fractional Partial Differential Equations. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2023. Lecture Notes in Networks and Systems, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-031-56304-1_19

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  • DOI: https://doi.org/10.1007/978-3-031-56304-1_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-56303-4

  • Online ISBN: 978-3-031-56304-1

  • eBook Packages: EngineeringEngineering (R0)

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