An analytical approach to reconstruct the initial distribution of a sub-diffusion model with time-fractional derivative

Optik ◽  
2016 ◽  
Vol 127 (21) ◽  
pp. 10238-10246
Author(s):  
Qian Zhan ◽  
Hui Wei
Keyword(s):  
Fractional Derivative ◽  
Diffusion Model ◽  
Analytical Approach ◽  
Initial Distribution ◽  
Time Fractional Derivative

scholarly journals Pricing Path-Independent Payoffs with Exotic Features in the Fractional Diffusion Model

2020 ◽  
Vol 4 (2) ◽  
pp. 16 ◽  
Author(s):  
Jean-Philippe Aguilar
Keyword(s):  
Fractional Derivative ◽  
Option Pricing ◽  
Diffusion Model ◽  
Financial Models ◽  
Convergent Series ◽  
Fractional Diffusion ◽  
Volatility Modeling ◽  
Time Fractional Derivative ◽  
Digital Options ◽  
Residue Theory

We provide several practical formulas for pricing path-independent exotic instruments (log options and log contracts, digital options, gap options, power options with or without capped payoffs …) in the context of the fractional diffusion model. This model combines a tail parameter governed by the space fractional derivative, and a subordination parameter governed by the time-fractional derivative. The pricing formulas we derive take the form of quickly convergent series of powers of the moneyness and of the convexity adjustment; they are obtained thanks to a factorized formula in the Mellin space valid for arbitrary payoffs, and by means of residue theory. We also discuss other aspects of option pricing such as volatility modeling, and provide comparisons of our results with other financial models.

scholarly journals Determination of the order of fractional derivative for subdiffusion equations

2020 ◽  
Vol 23 (6) ◽  
pp. 1647-1662
Author(s):  
Ravshan Ashurov ◽  
Sabir Umarov
Keyword(s):  
Fractional Derivative ◽  
Fixed Time ◽  
Time Instant ◽  
Observation Data ◽  
Additional Information ◽  
Fractional Modeling ◽  
Time Fractional Derivative ◽  
The Right ◽  
Right Order

Abstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.

Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?

Ground Water ◽  
2017 ◽  
Vol 55 (6) ◽  
pp. 857-870 ◽  
Author(s):  
Rhiannon M. Garrard ◽  
Yong Zhang ◽  
Song Wei ◽  
HongGuang Sun ◽  
Jiazhong Qian
Keyword(s):  
Fractional Derivative ◽  
Saturated Soils ◽  
Fractional Derivative Model ◽  
Time Fractional Derivative

Study of nonlinear Hirota-Satsuma coupled KdV and coupled mKdV system with time fractional derivative

Fractals ◽  
2021 ◽  
Author(s):  
Siddra Habib ◽  
Amreen Batool ◽  
Asad Islam ◽  
Muhammad Nadeem ◽  
Khaled A. Gepreel ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Time Fractional Derivative

scholarly journals Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19

2020 ◽  
Vol 138 ◽  
pp. 109959 ◽  
Author(s):  
Yong Zhang ◽  
Xiangnan Yu ◽  
HongGuang Sun ◽  
Geoffrey R. Tick ◽  
Wei Wei ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Mitigation Scenarios ◽  
Time Fractional Derivative
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