In the present article, we utilize the Conformable Double Laplace Transform Method (CDLTM) to get the exact solutions of a wide class of Conformable fractional differential in mathematical physics. The results obtained ...

The initial attached cell layer in multispecies biofilm growth is studied in this paper. The corresponding mathematical model leads to discuss a free boundary problem for a system of nonlinear hyperbolic partial differential ...

This paper deals with the numerical treatment of singularly perturbed parabolic reaction-diffusion initial boundary value problems. Introducing a fitting parameter into the asymptotic solution and applying average finite ...

A double delayed- HIV-1 infection model with optimal controls is taken into account. The proposed model consists of double-time delays and the following five compartments: uninfected cells CD4+ T cells, infected CD4+ T ...

This work presents a new approximation approach to solve the linear/nonlinear distributed order fractional differential equations using the Chebyshev polynomials. Here, we use the Chebyshev polynomials combined with the ...

In this paper, the interpolating moving least-squares (IMLS) method is discussed. The interpolating moving least square methodology is an effective technique for the approximation of an unknown function by using a set of ...

In this paper, we have proposed an efficient numerical method to solve a system linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM). Bernoulli wavelets have been generated ...

Here, we consider a fourth-order elliptic problem involving singularity and p(x)- biharmonic operator. Using Hardy's inequality, S+-condition, and Palais-Smale condition, the existence of weak solutions in a bounded domain ...

In this paper, an efficient numerical method is used to provide the approximate solution of distributed-order fractional partial differential equations (DFPDEs). The proposed method is based on the fractional integral ...

The basic motivation of the present study is to apply the local fractional Sumudu variational iteration method (LFSVIM) for solving nonlinear wave-like equations with variable coefficients and within local fractional ...

In this paper, we present a new fractional-order financial system (FOFS) with the new parameters. We study the synchronization for commensurate order of the fractional-order financial system with disturbance observer ...

In this paper, we first construct Alpert wavelet system and propose a computational method for solving a fractional nonlinear Fredholm integro-differential equation. Then we create an operational matrix of fractional ...

In this work, we employ a combination of variational iteration method (VIM) and Pad´e approximation method, called the VIM-Pad´e technique, to solve some nonlinear initial value problems and a delay differential equation ...

‎This paper aims to propose a high-order and accurate numerical scheme for the solution of the nonlinear diffusion equation with Riesz space fractional derivative. To this end, we first discretize the Riesz fractional ...

In this paper, we propose an efficient technique-based optimal homotopy analysis method with Green's function technique for the approximate solutions of nonlocal elliptic boundary value problems. We first transform the ...

The objective of this research is to propose a new multi-step method in tackling a system of nonlinear equations. The constructed iterative scheme achieves a higher rate of convergence whereas only one LU decomposition per ...

‎The present study aims are to analyze a delay tumor-immune fractional-order system to describe the rivalry among the immune system and tumor cells. Given that the dynamics of this system depend on the time delay parameter, ...

This paper is devoted to create new exact and numerical solutions of the generalized Korteweg-de Vries (GKdV) equation with ansatz method and Galerkin finite element method based on cubic B splines over finite elements. ...

In this paper, we propose a new numerical algorithm for the approximate solution of non-homogeneous fractional differential equation. Using this algorithm the fractional differential equations are transformed into a system ...

In this paper, a mixed reproducing kernel function (RKF) is introduced. The kernel function consists of piecewise polynomial kernels and polynomial kernels. On the basis of the mixed RKF, a new numerical technique is put ...