On the solution of two-sided fractional ordinary differential equations of Caputo type

DOI10.1515/fca-2016-0072zbMath1357.34014arXiv1701.04912OpenAlexW2564837231MaRDI QIDQ501517

Ma. Elena Hernández-Hernández, Vassili N. Kolokol'tsov

Publication date: 9 January 2017

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04912

zbMATH Keywords

stopping timeLévy processboundary pointFeller processgeneralized Caputo type derivativestwo-sided fractional equations

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Fractional derivatives and integrals (26A33) Fractional ordinary differential equations (34A08)

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Cites Work

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• Tempered fractional calculus
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Fractals and fractional calculus in continuum mechanics
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Generalised fractional evolution equations of Caputo type
• Chaos, fractional kinetics, and anomalous transport
• Formulation of Euler-Lagrange equations for fractional variational problems
• A predictor-corrector approach for the numerical solution of fractional differential equations
• The numerical solution of linear multi-term fractional differential equations: Systems of equations
• Existence of a solution for the fractional forced pendulum
• Some generalized fractional calculus operators and their applications in integral equations
• An historical perspective on fractional calculus in linear viscoelasticity
• On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations
• Finite difference approximations for two-sided space-fractional partial differential equations
• On stable processes with boundary conditions
• Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations
• On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type
• Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics
• On a class of differential equations with left and right fractional derivatives
• Potentials of Stable Processes
• On the First Exit Time of a Completely Asymmetric Stable Process from a Finite Interval
• On the Distribution of First Hits for the Symmetric Stable Processes
• Stochastic models for fractional calculus