On fractal-fractional waterborne disease model: A study on theoretical and numerical aspects of solutions via simulations

H Khan, J Alzabut, A Shah, ZY He, S Etemad… - Fractals, 2023 - World Scientific
Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water
and have a negative influence on human health. Due to the involvement of most countries in …

Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model

O Nikan, Z Avazzadeh, JAT Machado - Applied Mathematical Modelling, 2021 - Elsevier
The generalized Cattaneo model describes the heat conduction system in the perspective of
time-nonlocality. This paper proposes an accurate and robust meshless technique for …

An efficient numerical scheme to approach the time fractional black–scholes model using orthogonal gegenbauer polynomials

YE Aghdam, H Mesgarani, A Amin… - Computational …, 2024 - Springer
This paper proposes an efficient procedure to estimate the fractional Black–Scholes model
in time-dependent on the market prices of European options using the composition of the …

A novel collective algorithm using cubic uniform spline and finite difference approaches to solving fractional diffusion singular wave model through damping-reaction …

SW Yao, OA Arqub, S Tayebi, MS Osman, W Mahmoud… - Fractals, 2023 - World Scientific
Uses of time-fractional diffusion wave model (TFDWM) in its singular case with damping-
reaction terms are widely seen in classical physics applications, eg for the quantitative …

[HTML][HTML] High-accuracy numerical scheme for solving the space-time fractional advection-diffusion equation with convergence analysis

YE Aghdam, H Mesgarani, GM Moremedi… - Alexandria Engineering …, 2022 - Elsevier
In this paper, the space-time fractional advection-diffusion equation (STFADE) is considered
in the finite domain that the time and space derivatives are the Caputo fractional derivative …

[HTML][HTML] Stability and numerical analysis of the generalised time-fractional Cattaneo model for heat conduction in porous media

L Mohan, A Prakash - The European Physical Journal Plus, 2023 - Springer
This work investigates the generalised time-fractional Cattaneo model. The homotopy
perturbation transform technique is used to get the numerical solution of this model. The …

[HTML][HTML] A Robust and Versatile Numerical Framework for Modeling Complex Fractional Phenomena: Applications to Riccati and Lorenz Systems

WM Abdelfattah, O Ragb, M Salah, M Mohamed - Fractal and Fractional, 2024 - mdpi.com
The fractional differential quadrature method (FDQM) with generalized Caputo derivatives is
used in this paper to show a new numerical way to solve fractional Riccati equations and …

[HTML][HTML] Numerical estimation of the fractional advection–dispersion equation under the modified Atangana–Baleanu–Caputo derivative

M Partohaghighi, M Mortezaee, A Akgül, SM Eldin - Results in Physics, 2023 - Elsevier
The transport of contaminants is a crucial environmental issue, and accurate modeling of
this phenomenon is vital for developing effective strategies for its management. In this study …

A stability analysis for multi-term fractional delay differential equations with higher order

Z Yang, Q Li, Z Yao - Chaos, Solitons & Fractals, 2023 - Elsevier
As a widely used tool modeling some processes and systems in a variety of fields, fractional
delay differential equations (FDDEs) with higher order have attracted much attention of the …

The convergence analysis of the numerical calculation to price the time-fractional Black–Scholes model

H Mesgarani, M Bakhshandeh, YE Aghdam… - Computational …, 2023 - Springer
In this paper, the approximate solution u (x, t) of the temporal fractional Black–Scholes
model involving the time derivative in the Caputo sense with initial and boundary conditions …