Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems

T Guo, O Nikan, Z Avazzadeh, W Qiu - Computational and Applied …, 2022 - Springer
This paper proposes the alternating direction implicit (ADI) numerical approaches for
computing the solution of multi-dimensional distributed-order fractional integrodifferential …

Second-order accurate, robust and efficient ADI Galerkin technique for the three-dimensional nonlocal heat model arising in viscoelasticity

M Luo, W Qiu, O Nikan, Z Avazzadeh - Applied Mathematics and …, 2023 - Elsevier
This paper adopts an accurate and robust algorithm for the nonlocal heat equation having a
weakly singular kernel in three dimensions. The proposed method approximates the …

A localized hybrid kernel meshless technique for solving the fractional Rayleigh–Stokes problem for an edge in a viscoelastic fluid

Z Avazzadeh, O Nikan, AT Nguyen - Engineering Analysis with Boundary …, 2023 - Elsevier
This paper presents an efficient stabilized meshless technique with a hybrid kernel to
simulate the fractional Rayleigh–Stokes problem for an edge in a viscoelastic fluid. The …

Analytical solutions of the Predator–Prey model with fractional derivative order via applications of three modified mathematical methods

M Areshi, AR Seadawy, A Ali, AF Alharbi… - Fractal and …, 2023 - mdpi.com
We have investigated wave solutions of the Predator–Prey (PP) model with fractional
derivative order by novel three modified mathematical methods with the help of the …

Approximate solution of nonlinear time-fractional PDEs by Laplace residual power series method

H Aljarrah, M Alaroud, A Ishak, M Darus - Mathematics, 2022 - mdpi.com
Most physical phenomena are formulated in the form of non-linear fractional partial
differential equations to better understand the complexity of these phenomena. This article …

Solving and numerical simulations of fractional-order governing equation for micro-beams

A Yang, Q Zhang, J Qu, Y Cui, Y Chen - Fractal and Fractional, 2023 - mdpi.com
This paper applies a recently proposed numerical algorithm to discuss the deflection of
viscoelastic micro-beams in the time domain with direct access. A nonlinear-fractional order …

Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market

P Rahimkhani, Y Ordokhani… - … Methods in the Applied …, 2023 - Wiley Online Library
The main purpose of this work is to present a new numerical method based on Hahn hybrid
functions (HHFs) for solving of Black–Scholes option pricing distributed order time‐fractional …

A suitable hybrid meshless method for the numerical solution of time-fractional fourth-order reaction–diffusion model in the multi-dimensional case

A Habibirad, E Hesameddini, Y Shekari - Engineering Analysis with …, 2022 - Elsevier
This paper introduces a mixed meshless method for the numerical solution of time-fractional
fourth-order reaction–diffusion model in multi-dimensional case. By additional variable σ= Δ …

Hahn wavelets collocation method combined with Laplace transform method for solving fractional integro-differential equations

P Rahimkhani, Y Ordokhani - Mathematical Sciences, 2024 - Springer
The main idea of this paper is to establish the novel Hahn wavelets for solving fractional-
order integro-differential equations (FIDEs). First, we introduce Hahn wavelets and some of …

Variational fractional-order modeling of viscoelastic axially moving plates and vibration simulation

J Qu, Q Zhang, A Yang, Y Chen, Q Zhang - Communications in Nonlinear …, 2024 - Elsevier
Based on the thin plate theory and D'Alembert's principle to establish the equilibrium
equation for viscoelastic axially moving plates, this paper establishes the ternary governing …