Approximations of the Mittag-Leffler operator function with exponential accuracy and their applications to solving evolutionary equations with fractional time derivative

DOI10.1007/s11253-022-02096-0OpenAlexW4309683022WikidataQ115602716 ScholiaQ115602716MaRDI QIDQ2107794

Volodymyr L. Makarov, Ivan P. Gavrilyuk

Publication date: 5 December 2022

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-022-02096-0

zbMATH Keywords

evolutionary equationsfractional time derivativeapproximations of the mittag-leffler operator function

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Mittag-Leffler functions and generalizations (33E12) Linear differential equations in abstract spaces (34G10) Fractional ordinary differential equations (34A08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mittag-Leffler functions and their applications
• Numerical solution via Laplace transforms of a fractional order evolution equation
• A note on fractional derivatives and fractional powers of operators
• Strongly \(P\)-positive operators and explicit representations of the solutions of initial value problems for second-order differential equations in Banach space
• Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
• Exact and approximate solutions of some operator equations based on the Cayley transform
• Representation and approximation of the solution of an initial value problem for a first order differential equation in Banach spaces
• Quasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolation
• A Method for Solving Initial Value Problems for Linear Differential Equations in Hilbert Space Based on The Cayley Transform
• An algorithmic representation of fractional powers of positive operators
• Exponentially convergent method for an abstract integro - differential equation with fractional Hardy - Titchmarsh integral
• Exponentially Convergent Algorithms for Abstract Differential Equations
• Numerical Algorithm for Calculating the Generalized Mittag-Leffler Function
• The Cayley Transform as a Time Discretization Scheme
• Super Exponentially Convergent Approximation to the Solution of the Schrödinger Equation in Abstract Setting