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Mathematics 2019, 7(3), 265; https://doi.org/10.3390/math7030265

An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation

1
Department of Mathematics, Faculty of Science & Technology, Karnatak University, Dharwad 580003, India
2
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No, Etimesgut 406790, Turkey
3
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
*
Author to whom correspondence should be addressed.
Received: 20 December 2018 / Revised: 7 March 2019 / Accepted: 12 March 2019 / Published: 14 March 2019
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Abstract

The q -homotopy analysis transform method ( q -HATM) is employed to find the solution for the fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology. View Full-Text
Keywords: q-homotopy analysis transform method; fractional Kolmogorov–Petrovskii–Piskunov equation; Laplace transform q-homotopy analysis transform method; fractional Kolmogorov–Petrovskii–Piskunov equation; Laplace transform
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Veeresha, P.; Prakasha, D.G.; Baleanu, D. An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation. Mathematics 2019, 7, 265.

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