Mohammad Asif Arefin
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View article: Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method
Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method Open
The method of lines (MOL) is a solution procedure for solving partial differential equation (PDE) and the Crank-Nicholson method (CNM) is an implicit finite difference method, used to solve the elliptic equation and similar partial differe…
View article: Diverse soliton wave profile assessment to the fractional order nonlinear Landau-Ginzburg-Higgs and coupled Boussinesq-Burger equations
Diverse soliton wave profile assessment to the fractional order nonlinear Landau-Ginzburg-Higgs and coupled Boussinesq-Burger equations Open
The space–time fractional Landau-Ginzburg-Higgs equation and coupled Boussinesq-Burger equation describe the behavior of nonlinear waves in the tropical and mid-latitude troposphere, exhibiting weak scattering, extended connections, arisin…
View article: Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach
Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach Open
In engineering and applied sciences, several physical phenomena can be more precisely characterized by employing nonlinear fractional partial differential equations. The primary goal of this research is to examine the traveling wave soluti…
View article: Comprehensive dynamic-type multi-soliton solutions to the fractional order nonlinear evolution equation in ocean engineering
Comprehensive dynamic-type multi-soliton solutions to the fractional order nonlinear evolution equation in ocean engineering Open
Nonlinear fractional partial differential equations can explain a vast scope of engineering and science, like atomic physics, wireless transmission, nonlinear optics, acoustics, economics, materials science, control theory, plasma physics,…
View article: Utmost travelling wave phenomena to the fractional type nonlinear evolution equation in mathematical physics
Utmost travelling wave phenomena to the fractional type nonlinear evolution equation in mathematical physics Open
In applied physics and engineering, non-linear fractional types of partial differential equations become increasingly prominent as an estimation technique to explain a wide variety of non-linear phenomena. Throughout this study, we choose …
View article: Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method
Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method Open
The method of lines (MOL) is a solution procedure for solving partial differential equation (PDE) and the Crank-Nicholson method (CNM) is an implicit finite difference method, used to solve the elliptic equation and similar partial differe…
View article: Consistent travelling wave characteristic of space–time fractional modified Benjamin–Bona–Mahony and the space–time fractional Duffing models
Consistent travelling wave characteristic of space–time fractional modified Benjamin–Bona–Mahony and the space–time fractional Duffing models Open
Study on solitary wave phenomenon are closely related on the dynamics of the plasma and optical fiber system, which carry on broad range of wave propagation. The space–time fractional modified Benjamin–Bona–Mahony equation and Duffing mode…
View article: Existence and uniqueness solution analysis of time-fractional unstable nonlinear Schrödinger equation
Existence and uniqueness solution analysis of time-fractional unstable nonlinear Schrödinger equation Open
The time-fractional unstable nonlinear Schrödinger (NLS) equations capture the time evolution of disturbances within media, tailored for describing phenomena in unstable media to help model and understand the intricate dynamics of systems …
View article: Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation
Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation Open
In this work, a (2 + 1)-dimensional Ito equation is investigated, which represents the generalization of the bilinear KdV equation. Abundant double-periodic soliton solutions to the (2 + 1)-dimensional Ito equation are presented by the Hir…
View article: A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach
A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach Open
The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, …
View article: Utilizing the extended tanh-function technique to scrutinize fractional order nonlinear partial differential equations
Utilizing the extended tanh-function technique to scrutinize fractional order nonlinear partial differential equations Open
In a range of nonlinear fields, for example molecular biology, physics in plasma, quantum mechanics, elastic media, nonlinear optics, the surface of water waves, and others, many complicated nonlinear behaviors can be pronounced using nonl…
View article: Solitary wave solution to the space–time fractional modified Equal Width equation in plasma and optical fiber systems
Solitary wave solution to the space–time fractional modified Equal Width equation in plasma and optical fiber systems Open
Nonlinear fractional evolution equations play a crucial role in characterizing assorted complex nonlinear phenomena observed in different scientific fields, including plasma physics, quantum mechanics, elastic media, nonlinear optics, surf…
View article: Complex Dynamics and Chaos Control of a Discrete-Time Predator-Prey Model
Complex Dynamics and Chaos Control of a Discrete-Time Predator-Prey Model Open
The objective of this study is to investigate the complexity of a discrete predator-prey system. The discretization is achieved using the piecewise constant argument method. The existence and stability of equilibrium points, as well as tra…
View article: Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique Open
Nonlinear fractional partial differential equations are highly applicable for representing a wide variety of features in engineering and research, such as shallow-water, oceanography, fluid dynamics, acoustics, plasma physics, optical fibe…
View article: Sharp Bounds of Kulli–Basava Indices in Generalized Form for k-Generalized Quasi Trees
Sharp Bounds of Kulli–Basava Indices in Generalized Form for k-Generalized Quasi Trees Open
Molecular descriptors are a basic tool in the spectral graph, molecular chemistry, and various other fields of mathematics and chemistry. Kulli–Basava K B indices were initiated for chemical applications of various substances in chem…
View article: Stable and effective traveling wave solutions to the non-linear fractional Gardner and Zakharov–Kuznetsov–Benjamin–Bona–Mahony equations
Stable and effective traveling wave solutions to the non-linear fractional Gardner and Zakharov–Kuznetsov–Benjamin–Bona–Mahony equations Open
The space–time fractional Gardner and Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equations are used to explain the transmission of shallow water waves inside a water channel of uniform speed and constant depth. It moreover simulates w…
View article: Numerous explicit soliton solutions to the fractional simplified Camassa-Holm equation through two reliable techniques
Numerous explicit soliton solutions to the fractional simplified Camassa-Holm equation through two reliable techniques Open
In this study, the closed-form wave solutions has been examined to the space–time fractional simplified Camassa-Holm equation through two potential techniques, namely the sine-Gordon expansion approach and the extended tanh function scheme…
View article: Analysis of Reliable Solutions to the Boundary Value Problems by Using Shooting Method
Analysis of Reliable Solutions to the Boundary Value Problems by Using Shooting Method Open
This research aims to use the shooting method (SM) to find numerical solutions to the boundary value problems of ordinary differential equations (ODEs). Applied mathematics, theoretical physics, engineering, control, and optimization theor…
View article: A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods
A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods Open
The approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to t…
View article: Consistent travelling waves solutions to the non-linear time fractional Klein–Gordon and Sine-Gordon equations through extended tanh-function approach
Consistent travelling waves solutions to the non-linear time fractional Klein–Gordon and Sine-Gordon equations through extended tanh-function approach Open
In this study, the extended tanh-function method has been used to find further general travelling wave solutions for space-time fractional nonlinear partial differential equations, namely, the time fractional nonlinear Sine-Gordon equation…
View article: Analytical behavior of soliton solutions to the couple type fractional-order nonlinear evolution equations utilizing a novel technique
Analytical behavior of soliton solutions to the couple type fractional-order nonlinear evolution equations utilizing a novel technique Open
View article: Inelastic soliton wave solutions with different geometrical structures to fractional order nonlinear evolution equations
Inelastic soliton wave solutions with different geometrical structures to fractional order nonlinear evolution equations Open
The general time fractional Burger- Fisher (TF-BF) and the space–time regularized long-wave (STF-RLW) equations are considered as examples of gravitational water waves in cold plasma as well as so many areas. The above equations are used i…
View article: Novel Evaluation of Fuzzy Fractional Cauchy Reaction-Diffusion Equation
Novel Evaluation of Fuzzy Fractional Cauchy Reaction-Diffusion Equation Open
The present research correlates with a fuzzy hybrid approach merged with a new iterative transform method known as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we…
View article: Analyzing numerous travelling wave behavior to the fractional-order nonlinear Phi-4 and Allen-Cahn equations throughout a novel technique
Analyzing numerous travelling wave behavior to the fractional-order nonlinear Phi-4 and Allen-Cahn equations throughout a novel technique Open
Nonlinear fractional partial differential equations (NLFPDEs) are well suited for describing a broad range of factors in engineering and science, including plasma physics, optical fiber, acoustics, finance, turbulence, mechanical engineeri…
View article: New dynamical soliton propagation of fractional type couple modified equal-width and Boussinesq equations
New dynamical soliton propagation of fractional type couple modified equal-width and Boussinesq equations Open
View article: An analytical approach to the solution of fractional-coupled modified equal width and fractional-coupled Burgers equations
An analytical approach to the solution of fractional-coupled modified equal width and fractional-coupled Burgers equations Open
We opted to construct a traveling wave solution to the nonlinear space-time fractional coupled modified equal width (CMEW) equation and the space-time fractional-coupled Burgers equation, which are often used as an electro-hydro-dynamical …
View article: Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential‐Decay Kernel
Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential‐Decay Kernel Open
This study employs a newly developed methodology called the variational homotopy perturbation transformation method to study fractional acoustic wave equations. The motivation for this study is to extend the variational homotopy perturbati…
View article: The Analysis of Fractional‐Order System Delay Differential Equations Using a Numerical Method
The Analysis of Fractional‐Order System Delay Differential Equations Using a Numerical Method Open
To solve fractional delay differential equation systems, the Laguerre Wavelets Method (LWM) is presented and coupled with the steps method in this article. Caputo fractional derivative is used in the proposed technique. The results show th…
View article: Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique
Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique Open
The space-time fractional telegraph equation and the space-time fractional modified third-order Kdv equations are significant molding equations in theoretic physics, mathematical physics, plasma physics also other fields of nonlinear scien…
View article: Analytical behavior of weakly dispersive surface and internal waves in the ocean
Analytical behavior of weakly dispersive surface and internal waves in the ocean Open
The (2+1)-dimensional interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis is described by the space-time fractional Calogero-Degasperis (CD) and fractional potential Kadomstev-Petviashvili (PKP) equ…