Results 81 to 90 of about 1,369,996 (356)

Abstract differential equations and Caputo fractional derivative

Semigroup Forum, 2022
In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $ \in(0,1]$, and discuss the continuity of the respective solutions regarding the parameter $ $. I also present a study about the continuity of the Mittag-Leffler families of operators (for $ \in(0,1]$), induced by sectorial operators.
openaire   +2 more sources

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj   +1 more source

Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the Lp Space with the Framework of the Ψ-Caputo Derivative

Mathematics
In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in Lp space by using Jensen’s, Grönwall–Bellman’s, Hölder’s, and Burkholder–Davis–Gundy’s ...
Abdelhamid Mohammed Djaouti, Zareen A. Khan, Muhammad Imran Liaqat, Ashraf Al-Quran   +3 more
semanticscholar   +1 more source

On the Leibniz rule and Laplace transform for fractional derivatives

, 2019
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly.
Liu, Da-Yan, Tse, Peter W., Wang, Yong, Wei, Yiheng   +3 more
core   +1 more source

Dynamics of the Caputo fractional derivative

Fractional Calculus and Applied Analysis
Abstract 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. We will also show that a tuple of different iterates of a Caputo derivative multiple is disjoint hypercyclic.
Marina Murillo-Arcila, Alfred Peris, Álvaro Vargas-Moreno   +2 more
openaire   +1 more source

Approximations for the Caputo derivative (II)

, 2016
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation of the integral in the definition of the Caputo derivative. The asymptotic expansion formula of the Riemann sum approximation of the beta function and the first terms of the
Dimitrov, Yuri, Todorov, Venelin, Miryanov, Radan   +2 more
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Fractional variational problems with the Riesz–Caputo derivative [PDF]

Applied Mathematics Letters, 2012
AbstractIn this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz–Caputo derivative. First we prove a generalized Euler–Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative.
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Fractional hybrid systems involving '-Caputo derivative

Results in nonlinear analysis
This paper considers a coupled hybrid thermostat system driven by the à -Caputo fractional derivative in a Banach algebra. We employ a version of Darbo’s fixed-point theorem combined with the measure of noncompactness (MNC) technique to establish certain
Ma’mon, Abu Hammad, O. Zentar, M. Ziane, Alaa Alrawajfeh, Shameseddin Alshorm   +5 more
semanticscholar   +1 more source

Transient Charging of Mixed Ionic‐Electronic Conductors by Anomalous Diffusion

Advanced Materials, EarlyView.
This article explores charge transport in mixed ionic‐electronic conductors (MIECs) through electrochemical impedance spectroscopy and transient current analysis. Focusing on PEDOT:PSS, WO3, and n‐doped PBDF, it uncovers the impact of anomalous diffusion via fractional modeling. The study reveals key correlations that deepen understanding and guide the
Heyi Zhang, Gonzalo Rivera‐Sierra, Shirin Siahjani‐Gultekin, Jenifer Rubio‐Magnieto, Anis Allagui, Ignacio Sanjuán, David Franco, Antonio Guerrero, Enrique H. Balaguera, Juan Bisquert   +9 more
wiley   +1 more source

On Extended Caputo Fractional Derivative Operator

, 2017
The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly ...
Gauhar Rahman, Kottakkaran Sooppy Nisar, Muhammad Arshad   +2 more
openaire   +2 more sources