Results 81 to 90 of about 7,924 (216)
Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay
Discrete Dynamics in Nature and Society, 2014 This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously.
Abdulaziz Alofi +3 more
doaj +1 more source
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
wiley +1 more source
On Caputo modification of the Hadamard fractional derivatives [PDF]
Advances in Difference Equations, 2014 Abstract This paper is devoted to the study of Caputo modification of the Hadamard fractional derivatives. From here and after, by Caputo-Hadamard derivative, we refer to this modified fractional derivative (Jarad et al. in Adv. Differ. Equ. 2012:142, 2012, p.7). We present the generalization of the fundamental theorem of fractional calculus (
Yusuf Y. Gambo +3 more
openaire +1 more source
Journal of Function Spaces, 2021 A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite
Mostafa Abbaszadeh +3 more
doaj +1 more source
Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley +1 more source
, 2022 In this paper, we study the Ulam-Hyers-Mittag-Leffler stability for a linear fractional order differential equation with a fractional Caputo-type derivative using the fractional Fourier transform.
Sriramulu Sabarinathan +3 more
core +1 more source
Composition of Fractional Integral and Derivative Operators: Summarised in Tables
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
wiley +1 more source
In this paper, a high-order approximation to Caputo-type time-fractional diffusion equations involving an initial-time singularity of the solution is proposed.
Kumari, Shweta +3 more
core +1 more source
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative [PDF]
, 2011 This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function.
Changpin Li +2 more
core +1 more source
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley +1 more source