Time-fractional telegraph equation with ψ-Hilfer derivatives

Vieira, N.; Ferreira, Milton; Rodrigues, M. M.

doi:10.1016/j.chaos.2022.112276

Cited by 6 publications

(1 citation statement)

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“… 2022 ), wave propagation, solar particle transport (Vieira et al. 2022 ) and quantum mechanics (Zu and Yu 2022 ), to name a few. For extra information about the analysis and applications of FPDEs, the reader can consult (Ara et al.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

et al. 2023

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The time-fractional advection–diffusion reaction equation (TFADRE) is a fundamental mathematical model because of its key role in describing various processes such as oil reservoir simulations, COVID-19 transmission, mass and energy transport, and global weather production. One of the prominent issues with time fractional differential equations is the design of efficient and stable computational schemes for fast and accurate numerical simulations. We construct in this paper, a simple and yet efficient modified fractional explicit group method (MFEGM) for solving the two-dimensional TFADRE with suitable initial and boundary conditions. The proposed method is established using a difference scheme based on L1 discretization in temporal direction and central difference approximations with double spacing in spatial direction. For comparison purposes, the Crank–Nicolson finite difference method (CNFDM) is proposed. The stability and convergence of the presented methods are theoretically proved and numerically affirmed. We illustrate the computational efficiency of the MFEGM by comparing it to the CNFDM for four numerical examples including fractional diffusion and fractional advection–diffusion models. The numerical results show that the MFEGM is capable of reducing iteration count and CPU timing effectively compared to the CNFDM, making it well-suited to time fractional diffusion equations.

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Section: Introductionmentioning

confidence: 99%

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

et al. 2023

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Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

Lemnaouar

2024

Math Methods in App Sciences

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In this paper, we investigate the existence, uniqueness, and analysis of two types of ‐Mittag–Leffler–Ulam stabilities in a Volterra integro‐differential fractional differential equation that involves the ‐Hilfer operator. We utilize the Banach fixed‐point theorem to establish the existence and uniqueness of solutions. We examine the stability properties, including the ‐Mittag–Leffler–Ulam–Hyers ‐ and k‐Mittag–Leffler–Ulam–Hyers–Rassias ‐ stabilities, by employing the Grönwall–Bellman inequality. Additionally, we provide an example to confirm our findings.

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An improved lattice Boltzmann model for variable-order time-fractional generalized Navier-Stokes equations with applications to permeability prediction

Ren,

Lei,

Song

2024

Chaos, Solitons & Fractals

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Time-fractional telegraph equation with ψ-Hilfer derivatives

Cited by 6 publications

References 40 publications

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

An improved lattice Boltzmann model for variable-order time-fractional generalized Navier-Stokes equations with applications to permeability prediction

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