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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.

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 --- n/a --- fractional derivative of Riemann-Liouville type --- Green's functions --- Guo-Krasnosel'skii fixed point theorem in cones --- Arzelà-Ascoli Theorem --- Hermite-Hadamard inequality --- Caputo-Fabrizio fractional integral --- Jensen-Mercer inequality --- interval Hermite-Hadamard inequality --- interval Hermite-Hadamard-Fejér inequality --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér type inequality --- Hermite-Hadamard type inequalities

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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

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This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu.

Research & information: general --- Geography --- Ostrowski inequality --- Hölder's inequality --- power mean integral inequality --- n-polynomial exponentially s-convex function --- weight coefficient --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- half-discrete Hilbert-type inequality --- upper limit function --- Hermite-Hadamard inequality --- (p, q)-calculus --- convex functions --- trapezoid-type inequality --- fractional integrals --- functions of bounded variations --- (p,q)-integral --- post quantum calculus --- convex function --- a priori bounds --- 2D primitive equations --- continuous dependence --- heat source --- Jensen functional --- A-G-H inequalities --- global bounds --- power means --- Simpson-type inequalities --- thermoelastic plate --- Phragmén-Lindelöf alternative --- Saint-Venant principle --- biharmonic equation --- symmetric function --- Schur-convexity --- inequality --- special means --- Shannon entropy --- Tsallis entropy --- Fermi-Dirac entropy --- Bose-Einstein entropy --- arithmetic mean --- geometric mean --- Young's inequality --- Simpson's inequalities --- post-quantum calculus --- spatial decay estimates --- Brinkman equations --- midpoint and trapezoidal inequality --- Simpson's inequality --- harmonically convex functions --- Simpson inequality --- (n,m)-generalized convexity --- Ostrowski inequality --- Hölder's inequality --- power mean integral inequality --- n-polynomial exponentially s-convex function --- weight coefficient --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- half-discrete Hilbert-type inequality --- upper limit function --- Hermite-Hadamard inequality --- (p, q)-calculus --- convex functions --- trapezoid-type inequality --- fractional integrals --- functions of bounded variations --- (p,q)-integral --- post quantum calculus --- convex function --- a priori bounds --- 2D primitive equations --- continuous dependence --- heat source --- Jensen functional --- A-G-H inequalities --- global bounds --- power means --- Simpson-type inequalities --- thermoelastic plate --- Phragmén-Lindelöf alternative --- Saint-Venant principle --- biharmonic equation --- symmetric function --- Schur-convexity --- inequality --- special means --- Shannon entropy --- Tsallis entropy --- Fermi-Dirac entropy --- Bose-Einstein entropy --- arithmetic mean --- geometric mean --- Young's inequality --- Simpson's inequalities --- post-quantum calculus --- spatial decay estimates --- Brinkman equations --- midpoint and trapezoidal inequality --- Simpson's inequality --- harmonically convex functions --- Simpson inequality --- (n,m)-generalized convexity

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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.

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