Results 41 to 50 of about 974 (111)

Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

, 2011
We revisit the Mittag-Leffler functions of a real variable $t$, with one, two and three order-parameters $\{\alpha, \beta, \gamma\}$, as far as their Laplace transform pairs and complete monotonicty properties are concerned. These functions, subjected to
de Oliveira, Edmundo Capelas, Mainardi, Francesco, Vaz Jr, Jayme   +2 more
core   +1 more source

Optimal Control Strategies and Continuous Dependence for Stochastic Hilfer Fractional Systems With Delay: A Volterra‐Fredholm Integro‐Differential Approach

Optimal Control Applications and Methods, Volume 46, Issue 6, Page 2708-2726, November/December 2025.
The graphical abstract highlights our research on Sobolev Hilfer fractional Volterra‐Fredholm integro‐differential (SHFVFI) control problems for 1<ϱ<2$$ 1<\varrho <2 $$. We begin with the Hilfer fractional derivative (HFD) of order (1,2) in Sobolev type, which leads to Volterra‐Fredholm integro‐differential equations.
Marimuthu Mohan Raja, V. Vijayakumar, Chun‐Wei Tsai, Kalyana Chakravarthy Veluvolu   +3 more
wiley   +1 more source

A Study of Coupled Systems of ψ-Hilfer Type Sequential Fractional Differential Equations with Integro-Multipoint Boundary Conditions

Fractal and Fractional, 2021
In this paper, the existence and uniqueness of solutions for a coupled system of ψ-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions is investigated.
Ayub Samadi, Cholticha Nuchpong, Sotiris K. Ntouyas, Jessada Tariboon   +3 more
doaj   +1 more source

Revisiting the derivation of the fractional diffusion equation

, 2002
The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem.
Gorenflo, Rudolf, Mainardi, Francesco, Raberto, Marco, Scalas, Enrico   +3 more
core   +4 more sources

Modeling and Stability Analysis of Time‐Dependent Free‐Fall Motion in Random Environments

Discrete Dynamics in Nature and Society, Volume 2025, Issue 1, 2025.
This paper examines the stability of a fractional‐order model that describes the free‐fall motion of a football in changing environmental conditions. Traditional models often overlook memory effects and nonlocal influences like air resistance, humidity, and turbulence.
Alireza Hatami, Safoura Rezaei Aderyani, Reza Saadati, Mohammad Bagher Ghaemi, Cruz Vargas-De-León   +4 more
wiley   +1 more source

Ulam–Hyers–Rassias Stability of ψ-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays

Fractal and Fractional
The authors consider a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation (ψ-Hilfer FrOVIDE) that incorporates N-multiple variable time delays into the equation.
John R. Graef, Osman Tunç, Cemil Tunç
doaj   +1 more source

Physical Pictures of Transport in Heterogeneous Media: Advection-Dispersion, Random Walk and Fractional Derivative Formulations

, 2002
The basic conceptual picture and theoretical basis for development of transport equations in porous media are examined. The general form of the governing equations is derived for conservative chemical transport in heterogeneous geological formations, for
Anderson, Bear, Berkowitz, Berkowitz, Berkowitz, Berkowitz, Berkowitz, Berkowitz, Bouchaud, Brian Berkowitz, Chandrasekhar, Compte, Compte, Compte, Compte, Cushman, Dagan, Deng, Eggleston, Feehley, Garabedian, Gelhar, Glimm, Gnedenko, Haggerty, Harvey, Harvey Scher, Hatano, Hilfer, Jespersen, Joseph Klafter, Kenkre, Kinzelbach, Klafter, Klafter, Klafter, Koltermann, Kosakowski, Labolle, Labolle, Li, Lévy, Lévy, Mantegna, Mantegna, Margolin, Margolin, Matheron, Metzler, Metzler, Metzler, Metzler, Neuman, Oldham, Oppenheim, Ralf Metzler, Rubin, Samko, Scheidegger, Scheidegger, Scher, Scher, Scher, Shlesinger, Shlesinger, Silliman, Sposito, Zhang, Zumofen   +68 more
core   +1 more source

Trajectory Controllability of Fractional Neutral Stochastic Dynamical Systems of Order α ∈ (1, 2] With Deviating Argument

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
In this manuscript, we establish existence, uniqueness, and trajectory controllability for higher order noninstantaneous impulsive fractional neutral stochastic differential equations. First, solvability and uniqueness results are obtained using a fixed‐point approach with appropriate assumptions on nonlinear functions. Next, we deal with the strongest
Dhanalakshmi Kasinathan, Ravikumar Kasinathan, Ramkumar Kasinathan, Karthikeyan Shanmugasundaram, Dimplekumar Chalishajar, Theodore Simos   +5 more
wiley   +1 more source

Fractional calculus and continuous-time finance II: the waiting-time distribution

, 2000
We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al., and we point out its consistency with the behaviour observed in the waiting-time distribution ...
Butzer, Caputo, Clark, Enrico Scalas, Francesco Mainardi, Gel'fand, Gorenflo, Gorenflo, Gorenflo, Hilfer, Hughes, Klafter, Lefol, Mainardi, Mainardi, Mainardi, Mantegna, Marco Raberto, Montroll, Montroll, Montroll, Podlubny, Rudolf Gorenflo, Saichev, Samko, Schneider, Weiss, Weiss   +27 more
core   +3 more sources

Existence and Stability of Ulam–Hyers and Generalized Ulam–Hyers for the Generalized Langevin–Sturm–Liouville Equation Involving Generalized Liouville–Caputo Type

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper focuses on investigating the existence, uniqueness, and stability of Ulam–Hyers (U‐H) and generalized Ulam–Hyers (G‐U‐H) solutions for the generalized Langevin–Sturm–Liouville equation, which involves generalized Liouville–Caputo derivatives and antiperiodic boundary conditions. We can divide this manuscript into six parts. The first section
Muthaiah Subramanian, Bundit Unyong, Muath Awadalla, Watcharaporn Cholamjiak   +3 more
wiley   +1 more source