A class of traveling wave solutions for space–time fractional biological population model in mathematical physics

Akram, Ghazala; Batool, Fiza

doi:10.1007/s12648-017-1007-1

Cited by 26 publications

(5 citation statements)

References 18 publications

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“…and traveling wave solution (see [13], [14]) of the Landau-Lifshitz equation with external magnetic field…”

Section: Remark 23 In Lemma 22 We Construct the Transform That Ismentioning

confidence: 99%

Some New Solutions of the Landau-Lifshitz Equation in Cylindrical Symmetric System

Zhang

2020

JAMCS

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This paper is devoted to obtaining various explicit dynamic solutions of the Landau-Lifshitz equation in 2-dimensional cylindrical symmetric system. By suitably establishing explicit transformation, we here construct explicit dynamic solutions depending on the angle θ and time t for Landau-Lifshitz equation with anisotropy field or external magnetic field. Besides, we introduce certain indeterminate solution form of the Landau-Lifshitz equation by solving the indeterminate coefficients to derive explicit magnetic vortex or traveling wave solution. In this paper, we provide some specific examples and attain their some explicit dynamic solutions.

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“…and traveling wave solution (see [13], [14]) of the Landau-Lifshitz equation with external magnetic field…”

Section: Remark 23 In Lemma 22 We Construct the Transform That Ismentioning

confidence: 99%

Some New Solutions of the Landau-Lifshitz Equation in Cylindrical Symmetric System

Zhang

2020

JAMCS

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“…The FDEs are extremely suitable for modelling biological processes since it is generally concerned with biological models having memory, which seems to be a significant improvement among conventional integer order mathematical models, and it is connected to fractals, which are abundant in biological processes. In [52], researchers applied the ( ) ¢ G G expansion method to a class of traveling wave solutions of nonlinear onedimensional time dependent fractional biological population model. Agarwal et al [53] explored a PDES arising in biology and population genetics via semi analytical techniques.…”

Section: Introductionmentioning

confidence: 99%

Fractional spatial diffusion of a biological population model via a new integral transform in the settings of power and Mittag-Leffler nonsingular kernel

Rashid¹,

Kubra²,

Ullah³

2021

Phys. Scr.

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The current paper examines some novel and interesting aspects of the fractional biological population model involving the efficacious Atangana-Baleanu fractional derivative operator. It assists us in comprehending the dynamical techniques of population changes in biological population models and generates precise prognostication. This technique correlates with the Elzaki transform method and the homotopy perturbation method. The Elzaki transform is a modification of the classical Fourier Laplace transform. The approximate-analytical solutions of the biological population model are examined using the Elzaki transform homotopy perturbation method (ETHPM). The exact solution of the aforesaid scheme is being investigated in terms of the Mittag-Leffler function. The role of fractional-order on spatial diffusion of a biological population model is demonstrated in two and three-dimensional surface plots. The comparative analysis between exact and numerical solutions reveals the innovative features of the composite fractional derivative in the discussed model. Furthermore, the proposed approach is very powerful, reliable, wellorganized, and pragmatic for fractional PDEs and it might be extended to other physical processes.

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“…One of the important results of these solutions is soliton solution. The soliton solutions of NLEEs [1,2,3,4] are special type traveling waves and localized exponentially in certain directions on plane or space. It is well known that the Hirota bilinear forms are main ingredients in constructing soliton solutions [5].…”

Section: Introductionmentioning

confidence: 99%

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Yıldırım¹,

Yaşar²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we study lump-type solutions to a new extended (3+1)-dimensional nonlinear evolution equation which appears in the …eld of wave propagation in the nonlinear systems. We generate these types of solutions by considering the prime number p = 3 of the generalized Hirota bilinear operators. With the help of Maple symbolic computations, we retrieve twentytwo classes of lump-type solutions which are a special kind of rational function solutions, localized in all directions in the space and describe various dispersive wave phenomena. These lump-type solutions are derived from positive quadratic function solutions by using the generalized Hirota bilinear form of the considered model. The lump solutions are recovered along with the existence conditions: Analyticity, positivity and localization in all directions. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Lastly, the graphical simulations of the exact solutions are depicted.

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A class of traveling wave solutions for space–time fractional biological population model in mathematical physics

Cited by 26 publications

References 18 publications

Some New Solutions of the Landau-Lifshitz Equation in Cylindrical Symmetric System

Some New Solutions of the Landau-Lifshitz Equation in Cylindrical Symmetric System

Fractional spatial diffusion of a biological population model via a new integral transform in the settings of power and Mittag-Leffler nonsingular kernel

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

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