Comparative analysis of new approximate analytical method and Mohand variational transform method for the solution of wave-like equations with variable coefficients

Ahmad, Hijaz; Ozsahin, Dilber Uzun; Farooq, Umar; Fahmy, Mohamed Abdelsabour; Albalwi, M. Daher; Abu-Zinadah, Hanaa

doi:10.1016/j.rinp.2023.106623

Cited by 8 publications

(7 citation statements)

References 43 publications

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“…Case 1 yields the following families of traveling soliton solutions for (1): Family No. 1: When Y0 ≠ 0, we may infer the following array of traveling soliton solutions by using equations (10) and (12)in combination with the appropriate solutions to (9).…”

Section: Resultsmentioning

confidence: 99%

“…Family. 5: When ν = λ and μ = 0, we may infer the following array of traveling soliton solutions by using equations (10) and (12)in combination with the appropriate solutions to (9).…”

Section: Resultsmentioning

confidence: 99%

“…By considering case 3, we get the following families of traveling soliton solutions for (1): Family. 18: When Y < 0ν ≠ 0, then by utilizing equations (10) and (12) in conjunction with the corresponding solutions to (9), we deduce the subsequent array of traveling soliton solutions:…”

Section: Resultsmentioning

confidence: 99%

“…3. By seeking the homogeneous balance between the most dominant nonlinear term and the highest order derivative in equation (10), we determine the positive integer m as indicated in equation (8). 4.…”

Section: Procedures For M-edammentioning

confidence: 99%

“…Many researchers have been drawn to investigating nonlinear FPDEs because of their numerous applications in chemistry, acoustics, fluid dynamics, image processing, biology, physics, vibration, and control [5][6][7]. These nonlinear FPDEs have a high potential for use in a variety of domains, prompting academics to devote substantial time and effort to discovering analytical and numerical solutions [8][9][10][11][12]. To discover precise answers, Numerous efficient and trustworthy methods, including the unified method [13], exp-function approach [14], residual power series method [15], Kudryashov method [16], replicating kernel method [17], and others, have been developed by researchers.These approaches include the first integral method [18], Laplace Adomian decomposition method [19,20], natural transform decomposition method [21,22], homotopy analysis method [23], (G'/G)-enpension method [24][25][26], modified simple equation method [27], and EDAM [28,29].…”

Section: Introductionmentioning

confidence: 99%

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Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

Ullah,

Shah,

Abdeljawad

2024

Phys. Scr.

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The present research work presents the modified Extended Direct Algebraic Method (m-EDAM) to construct and analyze propagating soliton solutions for fractional Kolmogorov-Petrovskii-Piskunov Equation (FKPPE) which incorporates Caputo's fractional derivatives. The FKPPE has significance in various disciplines such as population growth, reaction-diffusion mechanisms, and mathematical biology. By leveraging the series form solution, the proposed m-EDAM determines plethora of travelling soliton solutions through the transformation of FKPPE into Nonlinear Ordinary Differential Equation (NODE). These soliton solutions shed light on propagation processes in the framework of the FKPPE model. Our study also offers some graphical representations that facilitate the characterization and investigation of propagation processes of the obtained soliton solutions which include kink, shock soliton solutions. Our work advances our understanding of complicated phenomena across multiple academic disciplines by fusing insights from mathematical biology and reaction-diffusion mechanisms.

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Section: Resultsmentioning

confidence: 99%

“…Family. 5: When ν = λ and μ = 0, we may infer the following array of traveling soliton solutions by using equations (10) and (12)in combination with the appropriate solutions to (9).…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Procedures For M-edammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

Ullah,

Shah,

Abdeljawad

2024

Phys. Scr.

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Fractional commensurate model on COVID‐19 with microbial co‐infection: An optimal control analysis

Vijayalakshmi,

Roselyn Besi,

Akgül

2024

Optim Control Appl Methods

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Crossover behaviors have always existed in the history of infectious pandemics due to a few distinct, erratic spread outlines. This research aims to investigate the crossover behavior of the proposed SVICR commensurate fractional model for the COVID‐19 delta variant, considering microbial coinfections. A mathematical model in terms of Atangana–Baleanu Caputo (ABC) category fractional integrals takes into account the co‐infection of mucormycosis in immunocompromised COVID‐19 patients caused by microbial infections. ABC operators preserve the intact history of the happenings under contemplation through its nonsingular kernel. It is observed that the framed five‐compartmental SVICR model is positively bounded on R5, the solution space. Two equilibrium points representing the survival and annihilation of sickness respectively are contributed by the single population N(t), which is counted in five dependent compartments: The bilinear growth rate of new additional infections from the contagious infectives over time ‘t’ is viewed through the threshold metric Lyapunov's stability function examines the parametric influences over the virulent spread globally. The significant focus is to investigate the Mucormycosis cases in COVID‐19 patients with underlying diabetic complications. Diabetes mellitus is the major concern for several coinfections among COVID‐19 recoveries. Aiming to minimalize the critical states, an Lagrangian–Hamiltonian optimum control structure is also performed for the SVICR model by introducing control variables in effect to tri‐control probes of minimized contact rates, persuasive vaccinations, and glycemic control of post recovered diabetic patients. The hike in the Severity of the ailment due to fungal pathogens is studied through numerical convergence of predictor–corrector scheme and simulations. Using estimated parametric values from the statistical data of mucormycosis and infections of COVID‐19 reported cases in India, the prominence of control effects are visualized graphically. To conclude, a complete qualitative analysis of the minimization problem is executed for different levels of control values. We avow that effective control intrusions would almost certainly decline the complexities associated with the viral pathogens.

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Dynamical study of groundwater systems using the new auxiliary equation method

Shahid,

Baber,

Shaikh

et al. 2024

Results in Physics

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Comparative analysis of new approximate analytical method and Mohand variational transform method for the solution of wave-like equations with variable coefficients

Cited by 8 publications

References 43 publications

Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

Fractional commensurate model on COVID‐19 with microbial co‐infection: An optimal control analysis

Dynamical study of groundwater systems using the new auxiliary equation method

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