Continuity of solutions to discrete fractional initial value problems
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Publication:710958
DOI10.1016/j.camwa.2010.03.040zbMath1197.39002OpenAlexW2077736465MaRDI QIDQ710958
Publication date: 23 October 2010
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2010.03.040
initial value problemdiscrete fractional calculuscontinuity with respect to initial conditionsdiscrete gronwall inequality
Integro-ordinary differential equations (45J05) Fractional derivatives and integrals (26A33) Additive difference equations (39A10)
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Cites Work
- Unnamed Item
- Unnamed Item
- Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
- Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation
- Basic theory of fractional differential equations
- Formulation of Euler-Lagrange equations for fractional variational problems
- Existence of positive solutions of nonlinear fractional differential equations
- Two-point boundary value problems for finite fractional difference equations
- Initial value problems in discrete fractional calculus
- Reviews of Nonlinear Dynamics and Complexity
- Positive solutions for boundary value problem of nonlinear fractional differential equation
- Analysis of fractional differential equations
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