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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

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• Reference Manager
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• 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.

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 --- n/a --- Riemann-Liouville fractional integral operator --- Burgers' equation --- predator-prey model --- the (m + 1/G')-expansion method --- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation

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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