A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative

Xia, Fangli; Jarad, Fahd; Hashemi, Mir Sajjad; Riaz, Muhammad Bilal

doi:10.1016/j.rinp.2022.105512

Cited by 43 publications

(10 citation statements)

References 31 publications

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“…Their findings demonstrate that the novel features of the capacitor microphone under consideration are recognized because the kernel may be configured more freely than in the prior mathematical formalism. The new local derivative, [ 46 ] Nuccis reduction and conservation laws, [ 47 ] fractional order, [ 48 ] and solutions of nonlinear models. [ 49 ] According to their results, the kernel may be designed more flexibly than in the previous mathematical formalism, allowing for the recognition of unique properties of the capacitor microphone under investigation.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of SARS‐CoV‐2 with Heart Attack Effected Patients and Bifurcation

Ahmad,

Abbas,

Inc

et al. 2024

Advanced Biology

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The aim of this study is to analyze and investigate the SARS‐CoV‐2 (SC‐2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the SC‐2 system is verified and test the proposed system with flip bifurcation. Also system is investigated for global stability using Lyponove first and second derivative functions. The existence, boundedness, and positivity of the SC‐2 is checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects of heart attack in united kingdom. Solutions for fractional order system are derived with the help of advanced tool FFO for different fractional values to verify the combine effect of COVID‐19 and heart patients. Simulation are carried out to see symptomatic as well as a symptomatic effects of SC‐2 in the United Kingdom as well as its global effects, also show the actual behavior of SC‐2 which will be helpful to understand the outbreak of SC‐2 for heart attack patients and to see its real behavior globally as well as helpful for future prediction and control strategies.

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Section: Introductionmentioning

confidence: 99%

Stability Analysis of SARS‐CoV‐2 with Heart Attack Effected Patients and Bifurcation

Ahmad,

Abbas,

Inc

et al. 2024

Advanced Biology

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“…Due to this complexity, obtaining analytical solutions is often a challenge, necessitating the evolution of various approaches to attain approximate or numerical solutions. In spite of this difficulty, methodologies such as the tanh technique [8], unified Riccati equation expansion method [9], enhanced modified extended tanh method [10], extended direct algebraic method [11], simplest equation method [12], direct mapping method [13], Hirota method [14], modification form of extended auxiliary equation mapping method [15], Kudryashov methods [16, 17],

\left({G}&amp;amp;#x0005E;{\prime }/G,1/G\right)

‐expansion method [18], ansatz transformations [19], Nucci's reduction method [20–22], sinh‐Gordon equation expansion, and (

\frac{G&amp;amp;#x0005E;{\prime }}{G&amp;amp;#x0005E;2}

)‐expansion function methods [23] have yielded analytical solutions for specific types of PDEs. These methods might be generally used after NLPDEs are converted into ordinary differential equations (ODEs) utilizing wave transformation.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive analysis of Fokas–Lenells equation using Lie symmetry method

Cinar,

Secer,

Sajjad Hashemi

et al. 2024

Math Methods in App Sciences

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This article extracts analytical solutions of the Fokas–Lenells equation describing pulse propagation in optical fibers and presents a comprehensive analysis of the analytical solutions. This paper focuses on deriving analytical, non‐perturbative solutions for the Fokas–Lenells equation by reducing it to a system of ordinary differential equations using the Lie symmetry method. Three generators for the Lie algebra are obtained, and three reductions are explored by combining vector generators. These algebraic structures provide a powerful framework for simplifying complex mathematical and physical problems by revealing underlying symmetries and patterns. The graphical representations of obtained solutions are rendered. Besides, the influence of parameters within the equation on the behavior of the solutions has been demonstrated in the figures. These results contribute to a deeper understanding of the Fokas–Lenells equation and have implications in various fields of physics and engineering.

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“…Hashemi et al [51] investigated the delay fractional differential equation of pantograph type discretized using fractional order alpert multiwavelets. Partohaghighi et al [52] investigated the fractional advection-dispersion equation numerical solution utilizing shifted Vieta-Lucas polynomials. Xia et al [53] investigated the reduction for addressing the new local derivative in the generalized nonlinear dispersive mK (m,n) equation.…”

Section: Introductionmentioning

confidence: 99%

Analytical analysis and heat transfer of CuO and MgO engine oil base nanofluid with the influence of dynamic viscosity, magnetic field, and convective boundary conditions

Rehman,

Khun,

Rezapour

et al. 2024

Z Angew Math Mech

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This research work investigates the semi‐numerical analysis and heat transfer of MHD 2D, Copper Oxide, and Magnesium oxide engine oil base nanofluid with the consider effect of dynamic viscosity and convective boundary conditions (BCs). The convective BCs and the effect of dynamic viscosity on an extensible surface are considered by the flow system. We converted a set of PDEs into NODEs by applying the appropriate transformations. Using the HAM, we solve this dimensionless coupled equation one for temperature and other for velocity. The impact of various parameters for both temperature and velocity are demonstrated, such as the slip parameter, magnetic parameter (MP), Eckert number (EN), PN, and dynamic viscosity. In response to changes in developing factors, the flow features, such as temperature profiles (TPs) and velocity profiles (VPs), are analyzed and simulated using a physical description. The results of this study add to our knowledge of how engine oil‐based nanofluids promote heat transmission and offer practical advice for thermal management and engineering applications.

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A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative

Cited by 43 publications

References 31 publications

Stability Analysis of SARS‐CoV‐2 with Heart Attack Effected Patients and Bifurcation

Stability Analysis of SARS‐CoV‐2 with Heart Attack Effected Patients and Bifurcation

A comprehensive analysis of Fokas–Lenells equation using Lie symmetry method

Analytical analysis and heat transfer of CuO and MgO engine oil base nanofluid with the influence of dynamic viscosity, magnetic field, and convective boundary conditions

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