Fractional Differential Equations: Theory, Methods and Applications
Nieto, Juan J.
Fractional Differential Equations: Theory, Methods and Applications - MDPI - Multidisciplinary Digital Publishing Institute 2019 - 1 electronic resource (172 p.)
Open Access
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.
Creative Commons
English
books978-3-03921-733-5 9783039217335 9783039217328
10.3390/books978-3-03921-733-5 doi
fractional wave equation dependence on a parameter conformable double Laplace decomposition method Riemann—Liouville Fractional Integration Lyapunov functions Power-mean Inequality modified functional methods oscillation fractional-order neural networks initial boundary value problem fractional p-Laplacian model order reduction ?-fractional derivative Convex Functions existence and uniqueness conformable partial fractional derivative nonlinear differential system conformable Laplace transform Mittag–Leffler synchronization delays controllability and observability Gramians impulses conformable fractional derivative Moser iteration method fractional q-difference equation energy inequality b-vex functions Navier-Stokes equation fractional-order system Kirchhoff-type equations Razumikhin method Laplace Adomian Decomposition Method (LADM) fountain theorem Hermite–Hadamard’s Inequality distributed delays Caputo Operator fractional thermostat model sub-b-s-convex functions fixed point theorem on mixed monotone operators singular one dimensional coupled Burgers’ equation generalized convexity delay differential system positive solutions positive solution fixed point index Jenson Integral Inequality integral conditions
Fractional Differential Equations: Theory, Methods and Applications - MDPI - Multidisciplinary Digital Publishing Institute 2019 - 1 electronic resource (172 p.)
Open Access
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.
Creative Commons
English
books978-3-03921-733-5 9783039217335 9783039217328
10.3390/books978-3-03921-733-5 doi
fractional wave equation dependence on a parameter conformable double Laplace decomposition method Riemann—Liouville Fractional Integration Lyapunov functions Power-mean Inequality modified functional methods oscillation fractional-order neural networks initial boundary value problem fractional p-Laplacian model order reduction ?-fractional derivative Convex Functions existence and uniqueness conformable partial fractional derivative nonlinear differential system conformable Laplace transform Mittag–Leffler synchronization delays controllability and observability Gramians impulses conformable fractional derivative Moser iteration method fractional q-difference equation energy inequality b-vex functions Navier-Stokes equation fractional-order system Kirchhoff-type equations Razumikhin method Laplace Adomian Decomposition Method (LADM) fountain theorem Hermite–Hadamard’s Inequality distributed delays Caputo Operator fractional thermostat model sub-b-s-convex functions fixed point theorem on mixed monotone operators singular one dimensional coupled Burgers’ equation generalized convexity delay differential system positive solutions positive solution fixed point index Jenson Integral Inequality integral conditions