Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations

We make use of the so-called Sumudu transform method (STM), a type of ordinary differential equations with both integer and noninteger order derivative. Firstly, we give the properties of STM, and then we directly apply it to fractional type ordinary differential equations, both homogeneous and inhomogeneous ones. We obtain exact solutions of fractional type ordinary differential equations, both homogeneous and inhomogeneous, by using STM. We present some numerical simulations of the obtained solutions and exhibit two-dimensional graphics by means of Mathematica tools. The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions

Qualitative Analysis on the Academic Work

Abstract: This article makes a qualitative analysis of what constitutes the academic work in its overlapping elements and processes. There is a joint analysis of theory and facts based on discourse analysis theory to observe intrinsic aspects that put creativity as an essential product of academic work, and extrinsic aspects necessary to establish trust and dignity as necessary assumptions to achieve its goal. We hope this approach become an available tool to protect creativity against abuses of power and to show how one builds a balanced academic work within an ethical dimension, preventing the construction of a fallacious product

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation

In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs) describing microtubules, by implementing the exp(−Φ(ξ))-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ))-Expansion Method not disappointing in the least, is found and declared highly efficient

Dynamic k-Struve Sumudu solutions for fractional kinetic equations

Abstract In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics

The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM) to some interesting nonhomogeneous fractional ordinary differential equations (FODEs). Finally, we use the solutions to form two-dimensional (2D) graphs, by using the symbolic algebra package Mathematica Program 7

Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations

We make use of the so-called Sumudu transform method (STM), a type of ordinary differential equations with both integer and noninteger order derivative. Firstly, we give the properties of STM, and then we directly apply it to fractional type ordinary differential equations, both homogeneous and inhomogeneous ones. We obtain exact solutions of fractional type ordinary differential equations, both homogeneous and inhomogeneous, by using STM. We present some numerical simulations of the obtained solutions and exhibit two-dimensional graphics by means of Mathematica tools. The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions

Sumudu Computation of the Transient Magnetic Field in a Lossy Medium

This research article aims at treating the transverse electromagnetic wave propagation in lossy media, labeled TEMP. Following the trail of works by Hussain and Belgacem, and Belgacem et al. towards getting the transient electric field solution of Maxwell’s equations, here we seek Sumudu transform based solution for transient magnetic field. Moreover, we feature connected interesting shifting properties of the Sumudu transform, some found useful in solving this very particular problem. Furthermore, we establish new analytico-numerical results, and exhibit graphical profiles of Sumudued ramp, gaussian pulse, and finite sinusoidal functions