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On the implementation of fractional homotopy perturbation transform method to the Emden–Fowler equations

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Abstract

In this paper, we use the homotopy perturbation transform method (HPTM) to offer an efficient semi-analytical technique for solving fractional Emden–Fowler equations. A mixture of Laplace transform, Caputo–Fabrizio derivative, and homotopy perturbation transformation process has the projected technique. To assess the efficacy of the suggested technique, test examples have been provided. The series have been used to represent semi-analytical solutions. Also, covered have the convergence position, estimation, and semi-analytical simulation results. The HPTM efficiently managed and controlled a series solution that quickly converges to a precise result in a narrow admissible region. The new findings essentially improve and simplify some of the previously published findings (see Malagia in Math. Comput. Simul. 190:362, 2021). By assigning appropriate values to free parameters, dynamical wave structures of some semi-analytical solutions are graphically demonstrated using 2-dimensional and 3-dimensional figures. Furthermore, various simulations are used to demonstrate the physical behaviors of the acquired solution with respect to fractional integer order.

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Authors and Affiliations

  1. Department of Mathematics, Bakhtiyarpur College of Engineering, Champapur, Dedaur, Bakhtiyarpur, 803 212, India

    Ajay Kumar

  2. Department of Mathematics, Government Engineering College, Buxar, Bakhtiyarpur, 803 212, India

    Raj Shekhar Prasad

  3. Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, Turkey

    Haci Mehmet Baskonus

  4. Departamento de Matematica Aplicada y Estadıstica, Universidad Politecnica de Cartagena, Hospital de Marina, Cartagena, 30203, Spain

    Juan Luis Garcia Guirao

  5. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Juan Luis Garcia Guirao

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  1. Ajay Kumar
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  2. Raj Shekhar Prasad
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  3. Haci Mehmet Baskonus
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  4. Juan Luis Garcia Guirao
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Correspondence to Haci Mehmet Baskonus.

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Kumar, A., Prasad, R.S., Baskonus, H.M. et al. On the implementation of fractional homotopy perturbation transform method to the Emden–Fowler equations. Pramana - J Phys 97, 123 (2023). https://doi.org/10.1007/s12043-023-02589-y

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  • DOI: https://doi.org/10.1007/s12043-023-02589-y

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