In numerical analysis, explicit and implicit approaches are used to obtain numerical approximations of time dependent ordinary and partial differential equations. Fractional order differential equations are used widely for finance market analysis. Implicit solution methods require more computational efforts and are complex to program. In order to overcome these difficulties, explicit method for fractional order differential equation has been introduced which is one of the most recently developed areas in the world of finance. The main aim of this paper is to investigate stability of Fractional Explicit method for qth order time fractional Black-Schols equation by the well known Fourier analysis method and a numerical experiment is presented for comparison of European call option prices for different values of ‘q’.

Keywords— Fractional calculus; Fractional Explicit Method; stability; European call options; time fractional Black-Schols equation; Fourier analysis.

MSC 2010 No.: 26A33, 65M06, 65TXX.

Introduction

In Numerical analysis, the use of Fractional calculus is increasing day by day. The field of fractional calculus is not new for mathematicians. It is as old as in the year 1695 , when L’Hopital sent a letter to Leibniz asking him an important question about the order of the derivative, “ What would be the result if order of derivative is
*…show more content…*

After introduction 1, the next section 2, will review the working of Fractional Explicit method. Section 3 is based on the stability analysis of the method. In section 4, there is a numerical experiment analyzing the performance of Fractional Explicit method for different values of ‘q’. Data for this experiment is taken from historical data section of NSE website of jet airways of the period from 1st November 2016 to 30th November 2016. Graphical representation is given for the more precise comparison. Finally in section 5 there is concluding remarks for the

Related

- Better Essays
## Isolation of Mitochondria

- 2221 Words
- 9 Pages

Cell fractionation is a very important procedure in cell biology and can be very useful for studying different organelles. By fractionating, we mean separating or dividing the cell into different component parts.

- 2221 Words
- 9 Pages

Better Essays - Decent Essays
## Separation Of A Mixture Of Hexane And Toluene

- 692 Words
- 3 Pages

Abstract The purpose of this experiment is to separate a mixture of hexane and toluene by collecting fractions through simple and fractional distillation. Because hexane’s boiling point is about 68°C and the boiling point of toluene is 111°C, the two compounds distill at different times. Pure products will be analyzed with gas chromatography to determine the success of the distillation. For easy separations, a simple distillation apparatus probably will suffice, but for more difficult separations, a fractional distillation apparatus will be used in this lab. The goal is to show that fractional distillation separates the two compounds more completely because less material is lost. In conclusion the fractional distillation indeed separates the two compound

- 692 Words
- 3 Pages

Decent Essays - Decent Essays
## Jesse Ernest Wilkins Jr

- 617 Words
- 3 Pages

Wilkins’s dissertation, completed under Magnus R. Hestenes, was titled Multiple Integral Problems in Parametric Form in the Calculus of Variations. He was the eighth black American, and one of the youngest Americans , to earn a Ph.D. degree in mathematics. A Rosenwald Scholarship enabled Wilkins to spend 1942 at the Institute for Advanced Study in Princeton, New Jerseys , as a postdoctoral research fellow.

- 617 Words
- 3 Pages

Decent Essays - Decent Essays
## Purpose Of An Unknown Solution Using Fractional Distillation

- 1031 Words
- 5 Pages

The purpose of this experiment was to perform a simple distillation as well as a fractional distillation and to determine the composition of an unknown solution using fractional distillation.

- 1031 Words
- 5 Pages

Decent Essays - Good Essays
## Fractional Distillation Organic Lab Report

- 2953 Words
- 12 Pages

With the purpose of the experiment being to identify the 30 mL of unknown liquid, the theoretical basis of simple and fractional distillation must be deconstructed and applied to the data obtained describing the liquid in question.

- 2953 Words
- 12 Pages

Good Essays - Better Essays
## Lab Report : Fractional Distillation And Gas Chromatography

- 1317 Words
- 6 Pages

The purpose of this lab is to investigate the processes that can be used to separate two volatile liquids in a mixture based on their chemical properties. This is accomplished by fractional distillation, which separates chemicals in a mixture by differentiating them by their boiling points at atmospheric pressure. Specifically in this lab, fractional distillation is used to separate an unknown mixture into its respective pure components. The components are then identified using gas chromatography, which is also telling of the purity of the extracts and success of the procedure. The procedure of this experiment was specified in lecture by Dr. Fjetland and in Gibert and Martin’s student lab manual, Experimental Organic Chemistry: A Miniscale and Microscale Approach, 6th Edition.

- 1317 Words
- 6 Pages

Better Essays - Better Essays
## Year 11 Chemistry Research Assignment

- 1833 Words
- 8 Pages

Describe the use of fractional distillation to separate the components of petroleum and identify the uses of each fraction obtained.

- 1833 Words
- 8 Pages

Better Essays - Decent Essays
## 2-Methylcyclohexanol Dehydration

- 644 Words
- 3 Pages

Fractional distillation uses a column filled with glass beads that improve the separation between the liquids that are being distilled. [6] The glass beads allow the refluxing liquid to condense, re-evaporate, and then condense again. [6] Fractional distillation is better used for separating mixtures of liquids that have close boiling point separations.[6] Due to the boiling point of 1-methylcyclohexene being 110°C, 3-methylcyclohexene being 104°C, and methylenecyclohexane being 102-103°C, fractional distillation was used instead of simple distillation. Even though the boiling points are different, they are still collected together, making them azeotropes. Due to this, they cannot be separated by fractional

- 644 Words
- 3 Pages

Decent Essays - Better Essays
## Suggestive Solutions Guide to Past Exam Papers

- 5119 Words
- 21 Pages

I have put some suggestive solutions or at least some hints for the past exam papers starting from year 2004. In so doing, I emphasize T 1, T 2 and T 3 of 2010, T 1 and T 2 year 2009, S1 and S2 of year 2008, S1 and S2 of year 2007, S1 and S2 of year 2006 — these past exam papers are more relevant to our current courses as we have used the same textbook, course outline and study guide. Please ignore the multiplier questions as those questions are not relevant for our ﬁnal exam. I also encourage my students to go through all those elive sessions (recorded by myself). These elive sessions will refresh your memory as well as help you to understand the

- 5119 Words
- 21 Pages

Better Essays - Decent Essays
## Bus 210 Week 4 Problem Solving Problem Analysis

- 437 Words
- 2 Pages

There are a lot of significant benefits of applying the numerical methods and programming into the job. According to the lecture note week 3, the bisection method has two main advantages such as “the method is guaranteed to converge” and “as iteration are conducted, the interval gets halves, therefore the error of the solution of the equation is guaranteed”. This method is very useful for any problem to solve for its root while we know two initial guesses. This numerical method is really simple to apply, plus we can solve the problems both by hand and MathLab. As we can see, there are a lab and two days of classes for how to use bisection equation. Moreover, the result from this is very satisfied because we can increase the number of iteration until the percentage of relative approximation error is acceptable or meet our desire.

- 437 Words
- 2 Pages

Decent Essays - Decent Essays
## Upwind Discretization Model Essay

- 901 Words
- 4 Pages

The central differencing method is used to find an expression for d2u/dx2 in the form ui-1 +ui+1

- 901 Words
- 4 Pages

Decent Essays - Good Essays
The purpose of this experiment was to separate a two component mixture using fractional distillation. Distillation is a process of vaporization than condensation of a substance, used primarily to separate substances from a mixture when there are different boiling points. Fractional distillation is when the mixture has multiple substances with similar boiling points, and a fractional column is used to create multiple vaporization/condensation cycles. Fractional distillation is important when two or more substances need to be separated, but they have similar boiling points.

- 781 Words
- 4 Pages

Good Essays - Satisfactory Essays
## Case Mw Petroleum

- 1167 Words
- 5 Pages

Firstly, there are some simplifications to be done to get all the necessary inputs for the Black & Scholes model. One approximation to be made is the estimation of the

- 1167 Words
- 5 Pages

Satisfactory Essays - Decent Essays
## Distillation Lab Report

- 1114 Words
- 5 Pages

By recording the temperature and distillate obtained during fractional distillation, a graph was plotted. At each point on the graph where temperature plateaus, a boiling point of a component of the unknown binary solution was reached. The graph obtained was ideal because two boiling points were determined to be around 82˚C and 124˚C. By comparing the boiling points to the list of known solvents, the first component was identified to be cyclohexane with

- 1114 Words
- 5 Pages

Decent Essays - Decent Essays
## Red Brand Canners ‚Äì Case Study

- 968 Words
- 4 Pages

Based on the above analysis we suggest that the solution provided by Coopers and Myers are

- 968 Words
- 4 Pages

Decent Essays