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

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...

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Main Authors:	Pundikala Veeresha, Doddabhadrappla Gowda Prakasha, Dumitru Baleanu
Format:	Article
Language:	English
Published:	MDPI AG 2019-03-01
Series:	Mathematics
Subjects:	q-homotopy analysis transform method fractional Kolmogorov–Petrovskii–Piskunov equation Laplace transform
Online Access:	http://www.mdpi.com/2227-7390/7/3/265

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spelling	doaj-ae169804c3bb45338e639bc14a8667a52020-11-25T02:26:32ZengMDPI AGMathematics2227-73902019-03-017326510.3390/math7030265math7030265An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov EquationPundikala Veeresha0Doddabhadrappla Gowda Prakasha1Dumitru Baleanu2Department of Mathematics, Faculty of Science & Technology, Karnatak University, Dharwad 580003, IndiaDepartment of Mathematics, Faculty of Science & Technology, Karnatak University, Dharwad 580003, IndiaDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 406790, Etimesgut, TurkeyThe 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.http://www.mdpi.com/2227-7390/7/3/265q-homotopy analysis transform methodfractional Kolmogorov–Petrovskii–Piskunov equationLaplace transform
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Pundikala Veeresha Doddabhadrappla Gowda Prakasha Dumitru Baleanu
spellingShingle	Pundikala Veeresha Doddabhadrappla Gowda Prakasha Dumitru Baleanu An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation Mathematics q-homotopy analysis transform method fractional Kolmogorov–Petrovskii–Piskunov equation Laplace transform
author_facet	Pundikala Veeresha Doddabhadrappla Gowda Prakasha Dumitru Baleanu
author_sort	Pundikala Veeresha
title	An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation
title_short	An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation
title_full	An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation
title_fullStr	An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation
title_full_unstemmed	An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation
title_sort	efficient numerical technique for the nonlinear fractional kolmogorov–petrovskii–piskunov equation
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-03-01
description	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.
topic	q-homotopy analysis transform method fractional Kolmogorov–Petrovskii–Piskunov equation Laplace transform
url	http://www.mdpi.com/2227-7390/7/3/265
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An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation

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