A novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solutio

A novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solu

The flow measurements have increased importance in the last decades due to the shortage of water resources resulting from climate changes that request high control of the available water needed for different uses. The classical technique of open channel flow measurement by the integrating-float method was needed for measuring flow in different locations when there were no available modern devices for different reasons, such as the cost of devices. So, the use of classical techniques was taken place to solve the problem. The present study examines the integrating float method and defines the parameters affecting the acceleration of floating spheres in flowing water that was analyzed using experimental measurements. The me

Many of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem

This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples

        This paper is concerned with the solution of the nanoscale structures consisting of the   with an effective mass envelope function theory, the electronic states of the  quantum ring are studied.  In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of  quantum rings are studied by the one electronic band Hamiltonian effective mass approximati

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.