Benedict Barnes
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View article: A methodological approach to solving the Korteweg–de Vries equation in its various forms
A methodological approach to solving the Korteweg–de Vries equation in its various forms Open
The Korteweg-de Vries (KdV) equation, an evolution-type nonlinear partial differential equation (PDE), describes the propagation of solitary water waves as observed in the literature. Finding the exact solution to such an equation usually …
View article: Exact solution of system of nonlinear fractional partial differential equations by modified semi-separation of variables method
Exact solution of system of nonlinear fractional partial differential equations by modified semi-separation of variables method Open
A system of nonlinear fractional partial differential equations (FPDEs) is widely used in applied sciences, especially for modeling fluid dynamics and polymer-related problems. Given their importance, finding solutions to these systems is …
The Modified Homogeneous Balance Method for solving fractional Cahn–Allen and equal width equations Open
This paper presents exact solutions to the Fractional Cahn–Allen (FC–A) and the Fractional Equal Width (FEW) equations using the Modified Homogeneous Balance Method (MHBM). The MHBM transforms the FC–A and FEW equations into fractional ord…
View article: The Exact Solution of the Fractional Burger’s Equation using the Modified Homogeneous Balance Method
The Exact Solution of the Fractional Burger’s Equation using the Modified Homogeneous Balance Method Open
In this paper, the Modified Homogeneous Balance Method, which is embedded with a fractional Riccati equation, is used to find exact solutions to the fractional Burger’s equation. Thus, this method incorporates a fractional Riccati equation…
View article: Fractional Gauss Hypergeometric Power Series Method for Solving Fractional Partial Differential Equations
Fractional Gauss Hypergeometric Power Series Method for Solving Fractional Partial Differential Equations Open
The Fractional Power Series Method (FPSM) is an effective and efficient method that offers an analytic method to find exact solution for Fractional Partial Differential Equations (FPDEs) in a functional space. In recent time, the FPSM has …
View article: The Analytic Methods for Solving the System of Fractional Order Brusselator Equations
The Analytic Methods for Solving the System of Fractional Order Brusselator Equations Open
Systems of fractional order Brusselator equations (SFBEs) have gained recent attention from researchers due to their relevance in the modeling of reaction‐diffusion processes in triple collision, enzymatic reactions, and plasma. Finding th…
View article: Modified Semiseparation of Variables Methods for Solving the System of Nonlinear Fractional Partial Differential Equations
Modified Semiseparation of Variables Methods for Solving the System of Nonlinear Fractional Partial Differential Equations Open
The system of nonlinear fractional partial differential equations (SNFPDEs) are widely used in modeling various phenomena in applied sciences. Consequently, finding the solutions to SNFPDEs has become paramount. Recently, an analytic metho…
View article: Modified Fractional Power Series Method for solving fractional partial differential equations
Modified Fractional Power Series Method for solving fractional partial differential equations Open
The literature revealed that the Fractional Power Series Method (FPSM), which uses the Mittag-Leffler function in one parameter, has been gainfully applied in obtaining the solutions of fractional partial differential equations (FPDEs) in …
Convexity Properties in Non-Newtonian Calculus and Their Applications Open
The study presented some results on convexity properties in non-Newtonian calculus. Also presented is the Jensen-Steffensen inequality in non-Newtonian calculus and some applications. The research was mainly on positive real numbers.
Fractional‐Order Delay Cobweb Model and Its Price Dynamics Open
This study compares the price dynamics of a Caputo fractional order delay differential cobweb model with existing cobweb models that have conformable fractional derivatives, Caputo fractional derivatives, and nonsingular kernel fractional …
The Analytic Solutions of the Fractional-Order Model for the Spatial Epidemiology of the COVID-19 Infection Open
This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and tem…
Price Dynamics of a Delay Differential Cobweb Model Open
The paper uses a new technique to find a unique solution to a delay differential cobweb model (formulated from a joint supply-demand function of price) with real model parameters via the Lambert W-function without considering any complex b…
Mathematical Modelling of the Spatial Epidemiology of COVID-19 with Different Diffusion Coefficients Open
This paper addresses the discrepancy between model findings and field data obtained and how it is minimized using the binning smoothing techniques: means, medians, and boundaries. Employing both the quantitative and the qualitative methods…
A 2-Phase Method for Solving Transportation Problems with Prohibited Routes Open
The Transportation Problem (TP) is a mathematical optimization technique which regulates the flow of items along routes by adopting an optimum guiding principle to the total shipping cost. However, instances including road hazards, traffic…
Using a Divergence Regularization Method to Solve an Ill-Posed Cauchy Problem for the Helmholtz Equation Open
The ill-posed Helmholtz equation with inhomogeneous boundary deflection in a Hilbert space is regularized using the divergence regularization method (DRM). The DRM includes a positive integer scaler that homogenizes the inhomogeneous bound…
Scattering of kinks in noncanonical sine-Gordon Model Open
In this paper, we numerically study the scattering of kinks in the noncanonical sine-Gordon model using Fourier spectral methods. The model depends on two free parameters, which control the localized inner structure in the energy density a…
Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi‐Reversibility Regularization Method Open
The Quasi‐Reversibility Regularization Method (Q‐RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace‐type operator in the …
The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems Open
This paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hada…
A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem Open
In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domai…
Vacuum polarization energy of the kinks in the sinh-deformed models Open
We compute the one-loop quantum corrections to the kink energies of the sinh-deformed $\phi^{4}$ and $\varphi^{6}$ models in one space and one time dimensions. These models are constructed from the well-known polynomial $\phi^{4}$ and $\va…
The Eigenspace Spectral Regularization Method for solving Discrete Ill-Posed Systems Open
In this paper, it is shown that discrete equations with Hilb ert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. These ill-p…