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In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications.

Research & information: general --- Mathematics & science --- Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm-Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Laplace transform --- Mittag-Leffler function --- Grünwald-Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness --- Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm-Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Laplace transform --- Mittag-Leffler function --- Grünwald-Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness

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

In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications.

Research & information: general --- Mathematics & science --- Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm–Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann–Liouville fractional derivative --- Hadamard–Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space–fractional Fokker–Planck operator --- time–fractional wave with the time–fractional damped term --- Laplace transform --- Mittag–Leffler function --- Grünwald–Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness --- n/a --- coupled hybrid Sturm-Liouville differential equation --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Mittag-Leffler function --- Grünwald-Letnikov scheme

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The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics.

Research & information: general --- Mathematics & science --- well posedness --- constrained variational control problem --- monotonicity --- pseudomonotonicity --- hemicontinuity --- multiple integral functional --- lower semicontinuity --- fractional differential equations --- fractional derivative of Riemann-Liouville type --- integral boundary value problems --- Green's functions --- Guo-Krasnosel'skii fixed point theorem in cones --- sublinearity and superlinearity --- Arzelà-Ascoli Theorem --- multi-objective programming --- fractional transportation problem --- intuitionistic fuzzy set --- parametric programming --- convex function --- h-convex function --- Hermite-Hadamard inequality --- Caputo-Fabrizio fractional integral --- Jensen inequality --- Jensen-Mercer inequality --- multiobjective programs with vanishing constraints --- semidefinite programming --- convexificators --- nonsmooth analysis --- constraint qualifications --- interval-valued function --- Riemann integral --- LR-convex interval-valued function --- interval Hermite-Hadamard inequality --- interval Hermite-Hadamard-Fejér inequality --- Lieb concavity theorem --- deformed exponential --- Pick function --- convexity of matrix --- low carbon inventory --- discount --- payment in advance --- price-sensitive demand --- emission reduction --- advances of SDO --- applications of SDO --- metaheuristic optimization --- nature-inspired algorithms --- optimization problems --- spiral dynamics optimization --- spiral-inspired optimization algorithms --- spiral paths --- (p,s)-convex fuzzy-interval-valued function --- fuzzy Riemann integral --- Jensen type inequality --- Schur type inequality --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér type inequality --- inverse geometric problem --- Laplace equation --- method of fundamental solution --- least-square problem --- micro resonator --- fractal --- multistability --- safe jump --- hidden attractor --- chaos --- basin of attraction --- LR-Harmonically convexity --- fractional integral operator --- Hermite-Hadamard type inequalities --- multimodal multi-objective optimization --- manta ray foraging optimizer --- non-dominated solution --- crowing distance --- engineering design problem --- optimal power flow --- renewable energy sources --- improved chaos game optimization --- TD-TI controller --- load frequency control --- electrical vehicles --- well posedness --- constrained variational control problem --- monotonicity --- pseudomonotonicity --- hemicontinuity --- multiple integral functional --- lower semicontinuity --- fractional differential equations --- fractional derivative of Riemann-Liouville type --- integral boundary value problems --- Green's functions --- Guo-Krasnosel'skii fixed point theorem in cones --- sublinearity and superlinearity --- Arzelà-Ascoli Theorem --- multi-objective programming --- fractional transportation problem --- intuitionistic fuzzy set --- parametric programming --- convex function --- h-convex function --- Hermite-Hadamard inequality --- Caputo-Fabrizio fractional integral --- Jensen inequality --- Jensen-Mercer inequality --- multiobjective programs with vanishing constraints --- semidefinite programming --- convexificators --- nonsmooth analysis --- constraint qualifications --- interval-valued function --- Riemann integral --- LR-convex interval-valued function --- interval Hermite-Hadamard inequality --- interval Hermite-Hadamard-Fejér inequality --- Lieb concavity theorem --- deformed exponential --- Pick function --- convexity of matrix --- low carbon inventory --- discount --- payment in advance --- price-sensitive demand --- emission reduction --- advances of SDO --- applications of SDO --- metaheuristic optimization --- nature-inspired algorithms --- optimization problems --- spiral dynamics optimization --- spiral-inspired optimization algorithms --- spiral paths --- (p,s)-convex fuzzy-interval-valued function --- fuzzy Riemann integral --- Jensen type inequality --- Schur type inequality --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér type inequality --- inverse geometric problem --- Laplace equation --- method of fundamental solution --- least-square problem --- micro resonator --- fractal --- multistability --- safe jump --- hidden attractor --- chaos --- basin of attraction --- LR-Harmonically convexity --- fractional integral operator --- Hermite-Hadamard type inequalities --- multimodal multi-objective optimization --- manta ray foraging optimizer --- non-dominated solution --- crowing distance --- engineering design problem --- optimal power flow --- renewable energy sources --- improved chaos game optimization --- TD-TI controller --- load frequency control --- electrical vehicles