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Fractional Differential Equations
Juan J. Nieto and Rosana Rodríguez-López
2019
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Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.
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Keywords
- ?-fractional derivative
- b-vex functions
- Caputo Operator
- conformable double Laplace decomposition method
- conformable fractional derivative
- conformable Laplace transform
- conformable partial fractional derivative
- controllability and observability Gramians
- Convex functions
- delay differential system
- delays
- dependence on a parameter
- distributed delays
- energy inequality
- existence and uniqueness
- fixed point index
- fixed point theorem on mixed monotone operators
- fountain theorem
- fractional p-Laplacian
- fractional q-difference equation
- fractional thermostat model
- fractional wave equation
- fractional-order neural networks
- fractional-order system
- generalized convexity
- Hermite–Hadamard’s Inequality
- impulses
- initial boundary value problem
- integral conditions
- Jenson Integral Inequality
- Kirchhoff-type equations
- Laplace Adomian Decomposition Method (LADM)
- Lyapunov functions
- Mittag–Leffler synchronization
- model order reduction
- modified functional methods
- Moser iteration method
- Navier-Stokes equation
- nonlinear differential system
- oscillation
- positive solution
- positive solutions
- Power-mean Inequality
- Razumikhin method
- Riemann—Liouville Fractional Integration
- singular one dimensional coupled Burgers’ equation
- sub-b-s-convex functions
Links
DOI: 10.3390/books978-3-03921-733-5Editions
