On ψ-Caputo Partial Hyperbolic Differential Equations with a Finite Delay

Article Mathematics, Applied

On the Stability of a Hyperbolic Fractional Partial Differential Equation

J. Vanterler da C. Sousa et al.

Summary: This paper introduces the psi-Riemann-Liouville fractional partial integral and the psi-Hilfer fractional partial derivative, and investigates the stabilities of solutions to a hyperbolic fractional partial differential equation in a Banach space using Gronwall inequality. An example is presented to illustrate the obtained results.

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS (2023)

添加到收藏夹

Article Mathematical & Computational Biology

A Novel Computational Tool for the Fractional-Order Special Functions Arising from Modeling Scientific Phenomena via Abu-Shady-Kaabar Fractional Derivative

M. Abu-Shady et al.

Summary: Recently, the Abu-Shady-Kaabar fractional derivative has been studied in detail and found to produce satisfactory results that are consistent with conventional definitions of fractional derivative. Additionally, the fractional solution to the Bessel equation has been discovered. Special functions play a crucial role in modeling phenomena in various scientific fields, making the development of a computational tool for computing fractional-order special functions necessary.

COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE (2022)

添加到收藏夹

Article Engineering, Multidisciplinary

A Generalized Definition of the Fractional Derivative with Applications

M. Abu-Shady et al.

Summary: In this work, a definition of the generalized fractional derivative (GFD) is proposed and it is shown to have better accuracy compared to the well-known definition of the conformable derivative. The GFD offers a simple tool for obtaining analytical solutions to problems in fractional calculus.

MATHEMATICAL PROBLEMS IN ENGINEERING (2021)

添加到收藏夹

Article Multidisciplinary Sciences

A New Class of Coupled Systems of Nonlinear Hyperbolic Partial Fractional Differential Equations in Generalized Banach Spaces Involving the ψ-Caputo Fractional Derivative

Zidane Baitiche et al.

Summary: The current study focuses on investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces using psi-Caputo partial fractional derivative. Various mathematical theorems, including Krasnoselskii-type fixed point theorem and Perov's fixed point theorem, were employed to prove the stability of solutions, with Urs's approach used specifically for Ulam-Hyers stability. Finally, examples were provided to illustrate the theoretical results.

SYMMETRY-BASEL (2021)

添加到收藏夹

Article Mathematics