Fractional oscillator equation -- transformation into integral equation and numerical solution

DOI10.1016/j.amc.2014.12.122zbMath1338.34012OpenAlexW2053308581MaRDI QIDQ299999

Mariusz Ciesielski, Tomasz Blaszczyk

Publication date: 23 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.12.122

zbMATH Keywords

numerical solutionfractional integral equationfractional Euler-Lagrange equationfractional oscillator

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Integral representations of solutions to PDEs (35C15) Fractional ordinary differential equations (34A08)

Related Items (13)

Nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions and Ulam-Hyers stability ⋮ Fractional optimal control problems on a star graph: optimality system and numerical solution ⋮ Existence of solutions for a mixed fractional boundary value problem ⋮ Exact and numerical solutions of the fractional Sturm-Liouville problem ⋮ On the existence and continuous dependence on parameter of solutions to some fractional Dirichlet problem with application to Lagrange optimal control problem ⋮ Three classes of fractional oscillators ⋮ On boundary value problems for impulsive fractional differential equations ⋮ On a fractional boundary value problem in a weighted space ⋮ Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives ⋮ The fractional Sturm-Liouville problem -- numerical approximation and application in fractional diffusion ⋮ Nonlinear boundary value problems for mixed-type fractional equations and Ulam-Hyers stability ⋮ A numerical method based on quadrature rules for \(\psi\)-fractional differential equations ⋮ The multiple composition of the left and right fractional Riemann-Liouville integrals - analytical and numerical calculations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete direct methods in the fractional calculus of variations
• Variational methods for the fractional Sturm-Liouville problem
• Numerical solution of fractional oscillator equation
• A numerical technique for solving a class of fractional variational problems
• An approximation of the analytical solution of the fractional Euler-Lagrange equation
• The Hahn quantum variational calculus
• Generalized vector calculus on convex domain
• On exact solutions of a class of fractional Euler-Lagrange equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Formulation of Euler-Lagrange equations for fractional variational problems
• Fractional sequential mechanics - models with symmetric fractional derivative.
• Existence of a weak solution for fractional Euler-Lagrange equations
• Expansion formula for fractional derivatives in variational problems
• Green's theorem for generalized fractional derivatives
• Numerical solution of fractional Sturm-Liouville equation in integral form
• A fractional calculus of variations for multiple integrals with application to vibrating string

This page was built for publication: Fractional oscillator equation -- transformation into integral equation and numerical solution