Results 11 to 20 of about 1,565,786 (254)

GENERALIZED CAPUTO-FABRIZIO FRACTIONAL DIFFERENTIAL EQUATION

Journal of Applied Analysis & Computation
In this paper, a generalization of the Caputo–Fabrizio fractional derivative is proposed. The purpose of this study is to derive a solution formula for ordinary differential equations with the generalized Caputo–Fabrizio fractional derivative.
M. Onitsuka, Iz-iddine El-Fassi
semanticscholar   +2 more sources

Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations [PDF]

Journal of Function Spaces, 2022
In this article, we prove some new uniqueness and Ulam-Hyers stability results of a nonlinear generalized fractional integro-differential equation in the frame of Caputo derivative involving a new kernel in terms of another function ψ .
Saeed M. Ali, W. Shatanawi, M. Kassim, Mohammed S Abdo, S. Saleh   +4 more
semanticscholar   +3 more sources

Langevin Equations with Generalized Proportional Hadamard–Caputo Fractional Derivative [PDF]

Computational Intelligence and Neuroscience, 2021
We look at fractional Langevin equations (FLEs) with generalized proportional Hadamard–Caputo derivative of different orders. Moreover, nonlocal integrals and nonperiodic boundary conditions are considered in this paper. For the proposed equations, the Hyres–Ulam (HU) stability, existence, and uniqueness (EU) of the solution are defined and ...
M. A. Barakat, Ahmed H. Soliman, Abd-Allah Hyder   +2 more
openaire   +2 more sources

Non-Instantaneous Impulsive BVPs Involving Generalized Liouville–Caputo Derivative [PDF]

Mathematics, 2022
This manuscript investigates the existence, uniqueness and Ulam–Hyers stability (UH) of solution to fractional differential equations with non-instantaneous impulses on an arbitrary domain. Using the modern tools of functional analysis, we achieve the required conditions. Finally, we provide an example of how our results can be applied.
Ahmed Salem, Sanaa Abdullah
openaire   +2 more sources

GENERALIZED LAPLACE TRANSFORM AND TEMPERED Ψ-CAPUTO FRACTIONAL DERIVATIVE

Mathematical Modelling and Analysis, 2023
In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived. The results are applied to find a solution to an initial value problem for a nonhomogeneous linear fractional differential equation with the tempered Ψ-Caputo fractional derivative of an
Milan Medveď, Michal Pospíšil
openaire   +4 more sources

Semi-Dynamical Systems Generated by Autonomous Caputo Fractional Differential Equations [PDF]

Vietnam Journal of Mathematics, 2021
An autonomous Caputo fractional differential equation of order $ \in(0,1)$ in $\mathbb{R}^d$ whose vector field satisfies a global Lipschitz condition is shown to generate a semi-dynamical system in the function space $\mathfrak{C}$ of continuous functions $f:\R^+\rightarrow \R^d$ with the topology uniform convergence on compact subsets.
Thai Son Doan, Peter E. Kloeden
openaire   +2 more sources

Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations

Fractal and Fractional, 2023
In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type of ...
Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
doaj   +1 more source

The existence, uniqueness, and stability analyses of the generalized Caputo-type fractional boundary value problems

AIMS Mathematics, 2023
In this article, we derive some novel results of the existence, uniqueness, and stability of the solution of generalized Caputo-type fractional boundary value problems (FBVPs).
P. R, Pushpendra Kumar, K. Nisar, V. Govindaraj   +3 more
semanticscholar   +1 more source

Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels

Axioms, 2022
We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean
Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres, Noura Yousfi   +3 more
doaj   +1 more source

Fractional Herglotz variational principles with generalized Caputo derivatives [PDF]

Chaos, Solitons & Fractals, 2017
We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscillator with time-depending mass and elasticity, and arbitrary memory effects.
Garra R., Taverna G. S., Torres D. F. M.
openaire   +3 more sources