The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of .

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The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation

In this letter, we present a hybrid computational approach established on local fractional Sumudu transform method and homotopy perturbation technique to procure the solution of the Klein–Gordon equations on Cantor sets. Four examples are provided to show the accuracy and coherence of the proposed technique. The outcomes disclose that the present computational approach is very user friendly and efficient to compute the nondifferentiable solution of Klein–Gordon equation involving local fractional operator.

A hybrid computational approach for Klein–Gordon equations on Cantor sets

We investigate a couple of different financial/economic models based on market equilibrium and option pricing with three different fractional derivatives in this paper. We obtain the fundamental solutions of the models by Sumudu transform and Laplace transform. We demonstrate our results by illustrative figures to point out the difference between the fractional operators that have power kernel, exponential kernel and Mittag-Leffler kernel. We prove the efficiency and accuracy of the Sumudu transform and decomposition series method constructed by the Laplace transform in providing the solutions of several different linear/nonlinear financial models by considering the theoretical results and illustrative applications. It seems that the proposed method is an efficient way to solve such problems that contain different types of fractional operators and one is able to point out the differences between these mentioned operators. One of the valuable features of the method is the possibility of using it in solving other similar equations including fractional derivatives having a singular or nonsigular kernel. This paper also suggests a good initiative and profitable tool for those who want to invest in these types of options either individually or institutionally.

New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives

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.

/pdf/sumudu-transform-method-for-analytical-solutions-of-ltthbypqc7.pdf

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

The key aim of this article is to present an efficient numerical algorithm based on local fractional homotopy perturbation Sumudu transform technique for solving local fractional heat-conduction equations in fractal media. The proposed technique is an effective combination of local fractional homotopy perturbation method (LFHPM) and local fractional Sumudu transform algorithm. The results obtained by using the suggested scheme show that the approach is straightforward to apply and very accurate. c ©2017 All rights reserved.

/pdf/an-efficient-computational-technique-for-local-fractional-2emp0kuei1.pdf

An efficient computational technique for local fractional heat conduction equations in fractal media

In this paper, we investigated solutions of heat equations by homotopy perturbation sumudu transform method (HPSTM) We drew graphics of these equations by means of programming language Mathematica

Homotopy perturbation Sumudu transform method for heat equations

In this paper, we have investigated solutions of heat equations by homotopy perturbation sumudu transform method (HPSTM). We have presented graphics of these equations by means of programming language Mathematica7.

Homotopy perturbation Sumudu transform for heat equations

In this paper, we studied to obtain numerical solutions of partial differential equations with variable coefficient by Sumudu Transform Method (STM). We applied to three examples this method. Then, we ploted 2D and 3D graphics of these equations by means of programming language Mathematica. In order to solve these differential equations which is ordinary and partial, the integral transforms such as the Laplace, Hankel and Fourier were unusually used and therefore there are several works on literature and applications of them. But it has few been given by using STM. And thus, in recent years STM has been an important places in applied sciences such as especially engineering, physics, physical sciences. Moreover, it is important for solving ordinary and partial differential equations which is linear and nonlinear.

The solutions of partial differential equations with variable coefficient by Sumudu Transform Method

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Homotopy perturbation Sumudu transform method for heat equations

Homotopy perturbation Sumudu transform for heat equations

The solutions of partial differential equations with variable coefficient by Sumudu Transform Method