Completely monotone functions and some classes of fractional evolution equations

DOI10.1080/10652469.2015.1039224zbMath1332.26011arXiv1502.04647OpenAlexW2153199111MaRDI QIDQ5262287

Emilia Bazhlekova

Publication date: 13 July 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.04647

zbMATH Keywords

Mittag-Leffler functioncompletely monotone functionBernstein functionfractional evolution equationdistributed order fractional derivative

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Fractional partial differential equations (35R11)

Related Items

Models of dielectric relaxation based on completely monotone functions ⋮ Integral representation of solutions of fractional system with distributed delays ⋮ On M-Wright transforms and time-fractional diffusion equations ⋮ Identification of a space-dependent source term in a nonlocal problem for the general time-fractional diffusion equation ⋮ Subordination principle for space-time fractional evolution equations and some applications ⋮ Fractional kinetic hierarchies and intermittency ⋮ Subordination approach to multi-term time-fractional diffusion-wave equations ⋮ Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives ⋮ Relaxation patterns and semi-Markov dynamics ⋮ Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation ⋮ Fractional Retarded Differential Equations Involving Mixed Nonlocal Plus Local Initial Conditions ⋮ Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation ⋮ Subordination in a class of generalized time-fractional diffusion-wave equations ⋮ Fractional diffusion equation with distributed-order Caputo derivative ⋮ Subordination principle for a class of fractional order differential equations ⋮ Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data

Cites Work

• Unnamed Item
• Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain
• Boundary value problems for multi-term fractional differential equations
• Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian
• New explicit formulas for the \(n\)th derivative of composite functions
• Viscoelastic flows with fractional derivative models: computational approach by convolutional calculus of Dimovski
• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
• Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density
• Distributed order calculus and equations of ultraslow diffusion
• On a Riemann–Liouville fractional analog of the Laplace operator with positive energy
• Vector-valued Laplace Transforms and Cauchy Problems
• Time-fractional Diffusion of Distributed Order
• The Two Forms of Fractional Relaxation of Distributed Order
• Completely monotonic functions
• The Mittag-leffler and related functions
• Mittag-Leffler Functions, Related Topics and Applications