Results 61 to 70 of about 4,852 (158)

Drivers of Hirola Antelope Diet Selection in Natural and Managed Habitat in Eastern Kenya

Ecology and Evolution, Volume 16, Issue 1, January 2026.
Hirola (Beatragus hunteri) populations in eastern Kenya consumed 17 forage species, favoring the grass Chloris virgata and the forbs Commelina benghalensis and C. diffusa. Nutrient analyses showed that natural habitats offered higher phosphorus, magnesium, and digestibility, whereas managed sites provided more sodium, potassium, and crude protein, with
Abdullahi H. Ali, S. Kivai
wiley   +1 more source

Radial Basis Function Neural Network With Resilient Backpropagation for Solving Fractional‐Order Chaotic Virotherapy Dynamics

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
The purpose of this work is to solve the fractional‐order model of chaotic virotherapy dynamics by executing a neural network scheme. The chaotic virotherapy dynamics is divided into four categories: uninfected tumor cells, infected tumor cells, immune cells, and virus‐free cells.
Zulqurnain Sabir, M. A. Abdelkawy, Muhammad Umar, Soheil Salahshour, Saira Bhatti, Smritijit Sen   +5 more
wiley   +1 more source

A Novel Fourth-Order Finite Difference Scheme for European Option Pricing in the Time-Fractional Black–Scholes Model

Mathematics
This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the α-order time-fractional Black–Scholes equation, where the Caputo fractional ...
Xin Cai, Yihong Wang
doaj   +1 more source

Memory‐Dependent Chaotic Dynamics and Stabilization of a Nonlinear Fractional‐Order Financial System With Optimal Control

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study presents an innovative nonlinear fractional‐order financial model that employs Caputo and Caputo–Fabrizio fractional derivatives to represent the dynamic interactions among interest rates, investment demand, price indices, and income/output. The model is formulated as a system of coupled nonlinear differential equations to encapsulate memory‐
Md. Asraful Islam, Razia Sultana, Payer Ahmed, Huaiqin Wu   +3 more
wiley   +1 more source

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Fractal and Fractional
The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of
Hongmei Zhang, Mengchen Zhang, Fawang Liu, Ming Shen   +3 more
doaj   +1 more source

Option Pricing in a Fractional Brownian Motion Environment [PDF]

The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian ...
Cipian Necula
core  

An Efficient Numerical Model for the Black–Scholes Equations

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, a novel numerical model for the Black–Scholes equations is developed. To address some potential issues that may arise when solving this equation using the conventional model, the original Black–Scholes equation is reformulated as a convection–diffusion equation. The Crank–Nicolson scheme is utilized to discretize the diffusion and source
Yan Zhou, Yunxing Zhang, Yufeng Xu
wiley   +1 more source

An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis

Fractal and Fractional
Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering.
Samuel M. Nuugulu, Frednard Gideon, Kailash C. Patidar   +2 more
doaj   +1 more source

A Framework for Derivative Pricing in the Fractional Black-Scholes Market [PDF]

The aim of this paper is to develop a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5.
Ciprian Necula
core  

Robust option replication for a Black-Scholes model extended with nondeterministic trends [PDF]

, 2012
Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model.
Kloeden, Peter E., Schoenmakers, John G. M.   +1 more
core