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It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Research & information: general --- Mathematics & science --- dynamic equations --- time scales --- classification --- existence --- necessary and sufficient conditions --- fractional calculus --- triangular fuzzy number --- double-parametric form --- FRDTM --- fractional dynamical model of marriage --- approximate controllability --- degenerate evolution equation --- fractional Caputo derivative --- sectorial operator --- fractional symmetric Hahn integral --- fractional symmetric Hahn difference operator --- Arrhenius activation energy --- rotating disk --- Darcy–Forchheimer flow --- binary chemical reaction --- nanoparticles --- numerical solution --- fractional differential equations --- two-dimensional wavelets --- finite differences --- fractional diffusion-wave equation --- fractional derivative --- ill-posed problem --- Tikhonov regularization method --- non-linear differential equation --- cubic B-spline --- central finite difference approximations --- absolute errors --- second order differential equations --- mild solution --- non-instantaneous impulses --- Kuratowski measure of noncompactness --- Darbo fixed point --- multi-stage method --- multi-step method --- Runge–Kutta method --- backward difference formula --- stiff system --- numerical solutions --- Riemann-Liouville fractional integral --- Caputo fractional derivative --- fractional Taylor vector --- kerosene oil-based fluid --- stagnation point --- carbon nanotubes --- variable thicker surface --- thermal radiation --- differential equations --- symmetric identities --- degenerate Hermite polynomials --- complex zeros --- oscillation --- third order --- mixed neutral differential equations --- powers of stochastic Gompertz diffusion models --- powers of stochastic lognormal diffusion models --- estimation in diffusion process --- stationary distribution and ergodicity --- trend function --- application to simulated data --- n-th order linear differential equation --- two-point boundary value problem --- Green function --- linear differential equation --- exponential stability --- linear output feedback --- stabilization --- uncertain system --- nonlocal effects --- linear control system --- Hilbert space --- state feedback control --- exact controllability --- upper Bohl exponent

Choose an application

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

It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Research & information: general --- Mathematics & science --- dynamic equations --- time scales --- classification --- existence --- necessary and sufficient conditions --- fractional calculus --- triangular fuzzy number --- double-parametric form --- FRDTM --- fractional dynamical model of marriage --- approximate controllability --- degenerate evolution equation --- fractional Caputo derivative --- sectorial operator --- fractional symmetric Hahn integral --- fractional symmetric Hahn difference operator --- Arrhenius activation energy --- rotating disk --- Darcy–Forchheimer flow --- binary chemical reaction --- nanoparticles --- numerical solution --- fractional differential equations --- two-dimensional wavelets --- finite differences --- fractional diffusion-wave equation --- fractional derivative --- ill-posed problem --- Tikhonov regularization method --- non-linear differential equation --- cubic B-spline --- central finite difference approximations --- absolute errors --- second order differential equations --- mild solution --- non-instantaneous impulses --- Kuratowski measure of noncompactness --- Darbo fixed point --- multi-stage method --- multi-step method --- Runge–Kutta method --- backward difference formula --- stiff system --- numerical solutions --- Riemann-Liouville fractional integral --- Caputo fractional derivative --- fractional Taylor vector --- kerosene oil-based fluid --- stagnation point --- carbon nanotubes --- variable thicker surface --- thermal radiation --- differential equations --- symmetric identities --- degenerate Hermite polynomials --- complex zeros --- oscillation --- third order --- mixed neutral differential equations --- powers of stochastic Gompertz diffusion models --- powers of stochastic lognormal diffusion models --- estimation in diffusion process --- stationary distribution and ergodicity --- trend function --- application to simulated data --- n-th order linear differential equation --- two-point boundary value problem --- Green function --- linear differential equation --- exponential stability --- linear output feedback --- stabilization --- uncertain system --- nonlocal effects --- linear control system --- Hilbert space --- state feedback control --- exact controllability --- upper Bohl exponent --- dynamic equations --- time scales --- classification --- existence --- necessary and sufficient conditions --- fractional calculus --- triangular fuzzy number --- double-parametric form --- FRDTM --- fractional dynamical model of marriage --- approximate controllability --- degenerate evolution equation --- fractional Caputo derivative --- sectorial operator --- fractional symmetric Hahn integral --- fractional symmetric Hahn difference operator --- Arrhenius activation energy --- rotating disk --- Darcy–Forchheimer flow --- binary chemical reaction --- nanoparticles --- numerical solution --- fractional differential equations --- two-dimensional wavelets --- finite differences --- fractional diffusion-wave equation --- fractional derivative --- ill-posed problem --- Tikhonov regularization method --- non-linear differential equation --- cubic B-spline --- central finite difference approximations --- absolute errors --- second order differential equations --- mild solution --- non-instantaneous impulses --- Kuratowski measure of noncompactness --- Darbo fixed point --- multi-stage method --- multi-step method --- Runge–Kutta method --- backward difference formula --- stiff system --- numerical solutions --- Riemann-Liouville fractional integral --- Caputo fractional derivative --- fractional Taylor vector --- kerosene oil-based fluid --- stagnation point --- carbon nanotubes --- variable thicker surface --- thermal radiation --- differential equations --- symmetric identities --- degenerate Hermite polynomials --- complex zeros --- oscillation --- third order --- mixed neutral differential equations --- powers of stochastic Gompertz diffusion models --- powers of stochastic lognormal diffusion models --- estimation in diffusion process --- stationary distribution and ergodicity --- trend function --- application to simulated data --- n-th order linear differential equation --- two-point boundary value problem --- Green function --- linear differential equation --- exponential stability --- linear output feedback --- stabilization --- uncertain system --- nonlocal effects --- linear control system --- Hilbert space --- state feedback control --- exact controllability --- upper Bohl exponent

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• Reference Manager
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During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Research & information: general --- Mathematics & science --- fractional evolution inclusions --- mild solutions --- condensing multivalued map --- arbitrary order differential equations --- multiple positive solution --- Perov-type fixed point theorem --- HU stability --- Caputo fractional derivative --- nonlocal --- integro-multipoint boundary conditions --- existence --- uniqueness --- Ulam-Hyers stability --- coupled system of fractional difference equations --- fractional sum --- discrete half-line --- non-instantaneous impulsive equations --- random impulsive and junction points --- continuous dependence --- Caputo–Fabrizio fractional differential equations --- Hyers–Ulam stability --- fractional derivative --- fixed point theorem --- fractional differential equation --- fractional sum-difference equations --- boundary value problem --- positive solution --- green function --- the method of lower and upper solutions --- three-point boundary-value problem --- Caputo’s fractional derivative --- Riemann-Liouville fractional integral --- fixed-point theorems --- Langevin equation --- generalized fractional integral --- generalized Liouville–Caputo derivative --- nonlocal boundary conditions --- fixed point --- fractional differential inclusions --- ψ-Riesz-Caputo derivative --- existence of solutions --- anti-periodic boundary value problems --- q-integro-difference equation --- fractional calculus --- fractional integrals --- Ostrowski type inequality --- convex function --- exponentially convex function --- generalized Riemann-liouville fractional integrals --- convex functions --- Hermite–Hadamard-type inequalities --- exponential kernel --- caputo fractional derivative --- coupled system --- impulses --- existence theory --- stability theory --- conformable derivative --- conformable partial derivative --- conformable double Laplace decomposition method --- conformable Laplace transform --- singular one dimensional coupled Burgers’ equation --- Green’s function --- existence and uniqueness of solution --- positivity of solution --- iterative method --- Riemann–Liouville type fractional problem --- positive solutions --- the index of fixed point --- matrix theory --- differential inclusions --- Caputo-type fractional derivative --- fractional integral --- time-fractional diffusion equation --- inverse problem --- ill-posed problem --- convergence estimates --- s-convex function --- Hermite–Hadamard inequalities --- Riemann–Liouville fractional integrals --- fractal space --- functional fractional differential inclusions --- Hadamard fractional derivative --- Katugampola fractional integrals --- Hermite–Hadamard inequality --- fractional q-difference inclusion --- measure of noncompactness --- solution --- proportional fractional integrals --- inequalities --- Qi inequality --- caputo-type fractional derivative --- fractional derivatives --- neutral fractional systems --- distributed delay --- integral representation --- fractional hardy’s inequality --- fractional bennett’s inequality --- fractional copson’s inequality --- fractional leindler’s inequality --- timescales --- conformable fractional calculus --- fractional hölder inequality --- sequential fractional delta-nabla sum-difference equations --- nonlocal fractional delta-nabla sum boundary value problem --- hadamard proportional fractional integrals --- fractional integral inequalities --- Hermite–Hadamard type inequalities --- interval-valued functions --- fractional evolution inclusions --- mild solutions --- condensing multivalued map --- arbitrary order differential equations --- multiple positive solution --- Perov-type fixed point theorem --- HU stability --- Caputo fractional derivative --- nonlocal --- integro-multipoint boundary conditions --- existence --- uniqueness --- Ulam-Hyers stability --- coupled system of fractional difference equations --- fractional sum --- discrete half-line --- non-instantaneous impulsive equations --- random impulsive and junction points --- continuous dependence --- Caputo–Fabrizio fractional differential equations --- Hyers–Ulam stability --- fractional derivative --- fixed point theorem --- fractional differential equation --- fractional sum-difference equations --- boundary value problem --- positive solution --- green function --- the method of lower and upper solutions --- three-point boundary-value problem --- Caputo’s fractional derivative --- Riemann-Liouville fractional integral --- fixed-point theorems --- Langevin equation --- generalized fractional integral --- generalized Liouville–Caputo derivative --- nonlocal boundary conditions --- fixed point --- fractional differential inclusions --- ψ-Riesz-Caputo derivative --- existence of solutions --- anti-periodic boundary value problems --- q-integro-difference equation --- fractional calculus --- fractional integrals --- Ostrowski type inequality --- convex function --- exponentially convex function --- generalized Riemann-liouville fractional integrals --- convex functions --- Hermite–Hadamard-type inequalities --- exponential kernel --- caputo fractional derivative --- coupled system --- impulses --- existence theory --- stability theory --- conformable derivative --- conformable partial derivative --- conformable double Laplace decomposition method --- conformable Laplace transform --- singular one dimensional coupled Burgers’ equation --- Green’s function --- existence and uniqueness of solution --- positivity of solution --- iterative method --- Riemann–Liouville type fractional problem --- positive solutions --- the index of fixed point --- matrix theory --- differential inclusions --- Caputo-type fractional derivative --- fractional integral --- time-fractional diffusion equation --- inverse problem --- ill-posed problem --- convergence estimates --- s-convex function --- Hermite–Hadamard inequalities --- Riemann–Liouville fractional integrals --- fractal space --- functional fractional differential inclusions --- Hadamard fractional derivative --- Katugampola fractional integrals --- Hermite–Hadamard inequality --- fractional q-difference inclusion --- measure of noncompactness --- solution --- proportional fractional integrals --- inequalities --- Qi inequality --- caputo-type fractional derivative --- fractional derivatives --- neutral fractional systems --- distributed delay --- integral representation --- fractional hardy’s inequality --- fractional bennett’s inequality --- fractional copson’s inequality --- fractional leindler’s inequality --- timescales --- conformable fractional calculus --- fractional hölder inequality --- sequential fractional delta-nabla sum-difference equations --- nonlocal fractional delta-nabla sum boundary value problem --- hadamard proportional fractional integrals --- fractional integral inequalities --- Hermite–Hadamard type inequalities --- interval-valued functions