Abstract Cauchy problems for the generalized fractional calculus

DOI10.1016/j.na.2021.112339zbMath1470.34157arXiv2006.09789OpenAlexW3150176718MaRDI QIDQ2033034

Giacomo Ascione

Publication date: 14 June 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.09789

zbMATH Keywords

contraction theoremGronwall inequalityBernstein functionsinverse subordinator

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Inequalities for sums, series and integrals (26D15) Fractional ordinary differential equations (34A08)

Related Items

Non-local solvable birth-death processes ⋮ A new approach to persistence and periodicity of logistic systems with jumps ⋮ On self-similar Bernstein functions and corresponding generalized fractional derivatives ⋮ Non-local logistic equations from the probability viewpoint ⋮ Time-non-local Pearson diffusions ⋮ Limit theorems for prices of options written on semi-Markov processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tempered fractional calculus
• General fractional calculus, evolution equations, and renewal processes
• Applications of inverse tempered stable subordinators
• A generalized Gronwall inequality and its application to a fractional differential equation
• On a nonlinear distributed order fractional differential equation
• Triangular array limits for continuous time random walks
• Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Recent applications of fractional calculus to science and engineering
• Time fractional equations and probabilistic representation
• Solutions of fractional logistic equations by Euler's numbers
• Modeling biological systems with an improved fractional Gompertz law
• Relaxation patterns and semi-Markov dynamics
• Convolution-type derivatives, hitting-times of subordinators and time-changed \(C_0\)-semigroups
• Well-posedness and numerical algorithm for the tempered fractional differential equations
• Vector-valued Laplace Transforms and Cauchy Problems
• A Gronwall inequality for a general Caputo fractional operator
• An Extension of the Fractional Gronwall Inequality
• Limit theorems for occupation times of Markov processes
• From diffusion to anomalous diffusion: A century after Einstein’s Brownian motion
• DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION
• Bernstein functions. Theory and applications
• An efficient method for solving fractional Hodgkin-Huxley model

This page was built for publication: Abstract Cauchy problems for the generalized fractional calculus