Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This Special Issue collects the latest results on differential/difference equations, the mathematics of networks, and their applications to engineering and physical phenomena. It features nine high-quality papers that were published with original research results. The Special Issue brings together mathematicians with physicists, engineers, as well as other scientists.

fractional discrete calculus --- discrete chaos --- Tinkerbell map --- bifurcation --- stabilization --- communication networks --- maximum flow --- network policies --- algorithms --- gas flow --- stress-sensitive porous media --- multiple hydraulic fractures --- vertical fractured well --- Output-feedback --- centralized control --- decentralized control --- closed-loop stabilization --- Hardy Cross method --- pipe networks --- piping systems --- hydraulic networks --- gas distribution --- multi-switching combination synchronization --- time-delay --- fractional-order --- stability --- Shehu transformation --- Adomian decomposition --- analytical solution --- Caputo derivatives --- (2+time fractional-order) dimensional physical models --- homotopy perturbation method --- variational iteration method --- Laplace transform method --- acoustic wave equations --- n/a

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem.

Technology: general issues --- fractional kinetic equation --- Riemann-Liouville fractional integral operator --- incomplete I-functions --- Laplace transform --- fractional differential equations --- fractional generalized biologic population --- Sumudu transform --- Adomian decomposition method --- Caputo fractional derivative --- operator theory --- time scales --- integral inequalities --- Burgers' equation --- reproducing kernel method --- error estimate --- Dirichlet and Neumann boundary conditions --- Caputo derivative --- Laplace transforms --- constant proportional Caputo derivative --- modeling --- Volterra-type fractional integro-differential equation --- Hilfer fractional derivative --- Lorenzo-Hartely function --- generalized Lauricella confluent hypergeometric function --- Elazki transform --- caputo fractional derivative --- predator-prey model --- harvesting rate --- stability analysis --- equilibrium point --- implicit discretization numerical scheme --- the (m + 1/G')-expansion method --- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation --- periodic and singular complex wave solutions --- traveling waves solutions --- chaotic finance --- fractional calculus --- Atangana-Baleanu derivative --- uniqueness of the solution --- fixed point theory --- shifted Legendre polynomials --- variable coefficient --- three-point boundary value problem --- modified alpha equation --- Bernoulli sub-equation function method --- rational function solution --- complex solution --- contour surface --- variable exponent --- fractional integral --- maximal operator

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations.

odd-order differential equations --- Kneser solutions --- oscillatory solutions --- deviating argument --- fourth order --- differential equation --- oscillation --- advanced differential equations --- p-Laplacian equations --- comparison theorem --- oscillation criteria --- thrid-order --- delay differential equations --- oscillations --- Riccati transformations --- fourth-order delay equations --- differential operator --- unit disk --- univalent function --- analytic function --- subordination --- q-calculus --- fractional calculus --- fractional differential equation --- q-differential equation --- second order --- neutral differential equation --- (1/G′)-expansion method --- the Zhiber-Shabat equation --- (G′/G,1/G)-expansion method --- traveling wave solutions --- exact solutions --- Adomian decomposition method --- Caputo operator --- Natural transform --- Fornberg–Whitham equations --- generalized proportional fractional operator --- nonoscillatory behavior --- damping and forcing terms --- Volterra integral equations --- operational matrix of integration --- multi-wavelets --- time scales --- functional dynamic equations --- highly oscillatory integral --- Chebyshev polynomial --- nearly singular --- Levin quadrature rule --- adaptive mesh refinement --- la Cierva’s autogiro --- la Cierva’s equation --- stability --- differential equation with periodic coefficients --- interpolating scaling functions --- hyperbolic equation --- Galerkin method --- higher-order --- neutral delay --- center of mass --- conformal metric --- geodesic --- hyperbolic lever law --- non-canonical differential equations --- second-order --- mixed type

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations.

Information technology industries --- odd-order differential equations --- Kneser solutions --- oscillatory solutions --- deviating argument --- fourth order --- differential equation --- oscillation --- advanced differential equations --- p-Laplacian equations --- comparison theorem --- oscillation criteria --- thrid-order --- delay differential equations --- oscillations --- Riccati transformations --- fourth-order delay equations --- differential operator --- unit disk --- univalent function --- analytic function --- subordination --- q-calculus --- fractional calculus --- fractional differential equation --- q-differential equation --- second order --- neutral differential equation --- (1/G′)-expansion method --- the Zhiber-Shabat equation --- (G′/G,1/G)-expansion method --- traveling wave solutions --- exact solutions --- Adomian decomposition method --- Caputo operator --- Natural transform --- Fornberg–Whitham equations --- generalized proportional fractional operator --- nonoscillatory behavior --- damping and forcing terms --- Volterra integral equations --- operational matrix of integration --- multi-wavelets --- time scales --- functional dynamic equations --- highly oscillatory integral --- Chebyshev polynomial --- nearly singular --- Levin quadrature rule --- adaptive mesh refinement --- la Cierva’s autogiro --- la Cierva’s equation --- stability --- differential equation with periodic coefficients --- interpolating scaling functions --- hyperbolic equation --- Galerkin method --- higher-order --- neutral delay --- center of mass --- conformal metric --- geodesic --- hyperbolic lever law --- non-canonical differential equations --- second-order --- mixed type