Results 71 to 80 of about 615,518 (166)

Spectral Collocation Method for Fractional Differential/Integral Equations with Generalized Fractional Operator

International Journal of Differential Equations, 2019
Generalized fractional operators are generalization of the Riemann-Liouville and Caputo fractional derivatives, which include Erdélyi-Kober and Hadamard operators as their special cases.
Qinwu Xu, Zhoushun Zheng
doaj   +1 more source

A Gronwall inequality for a general Caputo fractional operator

, 2017
In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo–Hadamard fractional derivative operators.
Almeida, Ricardo, Ricardo Almeida
core   +1 more source

Caputo-type modification of the Hadamard fractional derivatives [PDF]

, 2012
Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification
Thabet Abdeljawad, Abdeljawad, Thabet, Baleanu, Dumitru, Dumitru Baleanu, Jarad, Fahd, Fahd Jarad   +5 more
core   +1 more source

Weighted Spectral Properties of a Hadamard‐Type Fractional Operator

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this paper, we investigate a class of Hadamard‐type fractional operators from the viewpoint of functional analysis and spectral theory. The analysis is carried out on the bounded interval (1, R) within the weighted Hilbert space L2((1, R), dx/x), which naturally arises from the logarithmic structure associated with the Hadamard fractional derivative.
Muath Awadalla, Maryam G. Alshehri, Pengyu Chen   +2 more
wiley   +1 more source

Hyers–Ulam Stability of Hadamard Fractional Stochastic Differential Equations With Time Delay

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
We study the Hyers–Ulam stability of Hadamard fractional stochastic differential equations with a constant time delay, in which both the drift and the diffusion coefficients depend on the current state ϱ(κ) and on the delayed state ϱ(κ − τ), and the solution is subject to a prescribed history on [1 − τ, 1] together with a singular Hadamard‐type initial
Hend Aljahani, Foued Mtiri, Hamed Ould Sidi, Omar Naifar, Abdellatif Ben Makhlouf, Xian-Ming Gu   +5 more
wiley   +1 more source

On Caputo modification of Hadamard-type fractional derivative and fractional Taylor series

Advances in Difference Equations, 2020
In this paper a general framework is presented on some operational properties of Caputo modification of Hadamard-type fractional differential operator along with a new algorithm proposed for approximation of Hadamard-type fractional integral using Haar ...
Rashida Zafar, Mujeeb ur Rehman, Moniba Shams   +2 more
doaj   +1 more source

Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method

Fractal and Fractional
The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace transform (LT)
Awatif Muflih Alqahtani, Hamza Mihoubi, Yacine Arioua, Brahim Bouderah   +3 more
doaj   +1 more source

Dynamics of the Caputo fractional derivative [PDF]

In this article we analyse the dynamical behaviour of the Caputo complex fractional derivative. We prove that the Caputo complex fractional derivative operator is Devaney chaotic in the Mittag-Leffler Caputo space.
Murillo-Arcila, Marina, Vargas Moreno, Álvaro, Vargas-Moreno, Álvaro, Murillo Arcila, Marina, Peris Manguillot, Alfredo, Peris, A.   +5 more
core   +1 more source

Solvability of Tripled Langevin Fractional Differential Systems Involving ψ‐Caputo Derivatives Using Fixed Point Techniques

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This work is devoted to the study of a nonlinear tripled system of Langevin‐type fractional differential equations involving generalized ψ‐Caputo derivatives in the setting of Banach spaces. The proposed framework extends several existing results from finite‐dimensional and specialized functional spaces to more general infinite‐dimensional environments.
Hasanen A. Hammad, Manal Elzain Mohamed Abdalla, Bilal Bilalov   +2 more
wiley   +1 more source

A numerical framework based on piecewise Chebyshev cardinal functions for fractional integro-differential equations

Results in Applied Mathematics
In this study, we develop an operational matrix technique to address a set of fractional nonlinear integro-differential equations with the Caputo–Hadamard derivative. We utilize a family of the piecewise Chebyshev cardinal functions as basis functions in
S. Mansoori Aref, M.H. Heydari, M. Bayram   +2 more
doaj   +1 more source