Stability analysis and novel complex solutions to the malaria model utilising conformable derivatives

Ali, Asghar; Ahmad, Jamshad; Javed, Sara

doi:10.1140/epjp/s13360-023-03851-3

Cited by 16 publications

(4 citation statements)

References 41 publications

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“…In this section, we examine the stability property [35] for Eqs 1, 2. Understanding the stability of an equilibrium solution may be gained by linearizing the FNLPDE around it.…”

Section: Stability Analysismentioning

confidence: 99%

Complex solutions for nonlinear fractional partial differential equations via the fractional conformable residual power series technique and modified auxiliary equation method

Ali,

Nigar,

Nadeem

et al. 2023

Front. Phys.

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The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other fields of mathematical physics and engineering. This study has two main objectives. First, the main objective of this investigation is to solve the fractional-order nonlinear Gardner and Cahn–Hilliard equations by using the modified auxiliary equation method, which is not found in the literature. Second, the exact and approximate solutions of these equations are obtained by utilizing the fractional conformable residual power series algorithm and the modified auxiliary equation method. For the analytical and numerical solutions to two equations, we employ two separate techniques and establish consistency between the precise answers that are derived and the compatible numerical solution. To the best of our knowledge, this method of solving equations has never been investigated in this manner. The 2D and 3D contours have been defined using appropriate parametric values to support the physical compatibility of the results. The assessed findings suggested that the approach used in this study to recover inclusive and standard solutions is approachable, efficient, and faster in computing and can be considered a useful tool in resolving more complex phenomena that arise in the field of engineering, mathematical physics, and optical fiber.

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“…In this section, we examine the stability property [35] for Eqs 1, 2. Understanding the stability of an equilibrium solution may be gained by linearizing the FNLPDE around it.…”

Section: Stability Analysismentioning

confidence: 99%

Complex solutions for nonlinear fractional partial differential equations via the fractional conformable residual power series technique and modified auxiliary equation method

Ali,

Nigar,

Nadeem

et al. 2023

Front. Phys.

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“…The physical structures are better supported by these solutions of NLPDEs. In order to obtain the accurate solution for nonlinear physical models, various strong and effective methods, were developed and these methods are modified -expansion technique [ 8 , 9 ], the -expansion function technique [ 10 , 11 ], the first integral technique [ 12 , 13 ], the Hirota bilinear transformation technique [ 14 – 16 ], the kather technique [ 17 ], the sin-Gordon expansion technique [ 18 ], the sin-cosine technique [ 19 ] and several others [ 20 , 21 ]. Recently, other strategies are also taken into consideration for a range of lump solutions [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

“…-expansion function technique [10,11], the first integral technique [12,13], the Hirota bilinear transformation technique [14][15][16], the kather technique [17], the sin-Gordon expansion technique [18], the sin-cosine technique [19] and several others [20,21]. Recently, other strategies are also taken into consideration for a range of lump solutions [22].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation and investigation of soliton solutions and chaotic behavior to a stochastic nonlinear Schrödinger model with a random potential

Ali,

Ahmad,

Javed

et al. 2024

PLoS ONE

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The stochastic nonlinear Schrödinger model (SNLSM) in (1+1)-dimension with random potential is examined in this paper. The analysis of the evolution of nonlinear dispersive waves in a totally disordered medium depends heavily on the model under investigation. This study has three main objectives. Firstly, for the SNLSM, derive stochastic precise solutions by using the modified Sardar sub-equation technique. This technique is efficient and intuitive for solving such models, as shown by the generated solutions, which can be described as trigonometric, hyperbolic, bright, single and dark. Secondly, for obtaining numerical solutions to the SNLSM, the algorithms described here offer an accurate and efficient technique. Lastly, investigate the phase plane analysis of the perturbed and unperturbed dynamical system and the time series analysis of the governing model. The results show that the numerical and analytical techniques can be extended to solve other nonlinear partial differential equations in physics and engineering. The results of this study have a significant impact on how well we comprehend how solitons behave in physical systems. Additionally, they may serve as a foundation for the development of improved numerical techniques for handling challenging nonlinear partial differential equations.

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“…The study aims to obtain a novel soliton to an FCKOM via a unified technique (UT) [ 26 ] is a novel analytical technique for solving FPDEs. Also, investigate the phase portrait analysis for the perturbed and nonperturbed dynamical system which is obtained by the nonlinear ordinary differential equation (NODE) of FCKOM.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of chaos, bifurcation analysis and soliton solutions to a Konno-Onno model

Chahlaoui,

Ali,

Ahmad

et al. 2023

PLoS ONE

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The fractional coupled Konno-Onno model, which is frequently used in numerous fields of scientific and engineering disciplines, is being investigated in the current study in order to gain an understanding of complex phenomena and systems. The two main goals of this study are to be accomplished. Firstly, the research aims to identify novel solitons for the fractional coupled Konno-Onno model using the unified technique, which is currently absent from the literature. Secondly, a novel strategy that hasn’t been previously investigated is phase portrait analysis for both perturbed and non-perturbed dynamical systems. The current study uses appropriate parametric values in phase plane analysis, 2D, 3D, and density plots to ensure the results are physically compatible. The results validate the claim that the technique used in this research to produce complete and uniform responses is not only simple to use and effective, but also substantially faster in computing. The technique is useful for resolving more complex phenomena that arise in engineering and mathematical physics.

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Stability analysis and novel complex solutions to the malaria model utilising conformable derivatives

Cited by 16 publications

References 41 publications

Complex solutions for nonlinear fractional partial differential equations via the fractional conformable residual power series technique and modified auxiliary equation method

Complex solutions for nonlinear fractional partial differential equations via the fractional conformable residual power series technique and modified auxiliary equation method

Numerical simulation and investigation of soliton solutions and chaotic behavior to a stochastic nonlinear Schrödinger model with a random potential

Dynamical behavior of chaos, bifurcation analysis and soliton solutions to a Konno-Onno model

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