Results 81 to 90 of about 58,917 (294)

Ulam‐type stability of ψ− Hilfer fractional‐order integro‐differential equations with multiple variable delays

Asian Journal of Control, EarlyView.
Abstract We study a nonlinear ψ−$$ \psi - $$ Hilfer fractional‐order delay integro‐differential equation ( ψ−$$ \psi - $$ Hilfer FrODIDE) that incorporates N−$$ N- $$ multiple variable time delays. Utilizing the ψ−$$ \psi - $$ Hilfer fractional derivative ( ψ−$$ \psi - $$ Hilfer‐FrD), we investigate the Ulam–Hyers––Rassias (U–H–R), semi‐Ulam–Hyers ...
Cemil Tunç, Osman Tunç
wiley   +1 more source

Application of Newton’s polynomial interpolation scheme for variable order fractional derivative with power-law kernel

Scientific Reports
This paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional derivatives, such as the Caputo derivative, the Caputo–Fabrizio derivative, the Atangana–Baleanu fractal and fractional ...
S Naveen, V Parthiban
doaj   +1 more source

Numerical Methods for Solving Fractional Differential Equations [PDF]

, 2018
Department of Mathematical SciencesIn this thesis, several efficient numerical methods are proposed to solve initial value problems and boundary value problems of fractional di???erential equations.
Kim, Keon Ho
core  

Towards Fractional Gradient Elasticity

, 2013
An extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe power-law type of non-locality is discussed. Two phenomenological possibilities are explored.
Aifantis, Elias C., Tarasov, Vasily E.
core   +1 more source

Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

, 2020
This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the ψ–Caputo fractional derivative in Banach spaces.
C. Derbazi, Z. Baitiche, M. Benchohra
semanticscholar   +1 more source

No‐regret and low‐regret control for a weakly coupled abstract hyperbolic system

Asian Journal of Control, EarlyView.
Abstract This paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave‐like phenomena and complexity, become even more challenging with weak coupling between subsystems.
Meriem Louafi, Mohammed Messaoudi, Thabet Abdeljawad, Fahd Jarad   +3 more
wiley   +1 more source

A new Definition of Fractional Derivative and Fractional Integral [PDF]

Kirkuk Journal of Science, 2018
In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
doaj   +1 more source

Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations

, 2018
In this paper, we propose and analyze a spectral Chebyshev-Legendre approximation for fractional order integro-differential equations of Fredholm type. The fractional derivative is described in the Caputo sense.
Babolian, E., Javadi, S., Moradi, E., Yousefi, A.   +3 more
core   +1 more source

A Fractional-Order Investigation of Vaccinated SARS-CoV-2 Epidemic Model with Caputo Fractional Derivative [PDF]

, 2022
Badr Saad T. Alkahtani
openalex   +1 more source

On the generalized fractional derivatives and their Caputo modification

The Journal of Nonlinear Sciences and Applications, 2017
Summary: In this manuscript, we define the generalized fractional derivative on \(AC^n_\gamma [a, b]\), the space of functions defined on \([a,b]\) such that \(\gamma^{n-1}f\in AC[a, b]\), where \(\gamma=x^{1-p}\frac{d}{dx}\). We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo ...
Jarad, F., Abdeljawad, T., Baleanu, D.
openaire   +3 more sources