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This book is a compilation of works covering applied mathematical methods and their applications in complex engineering problems. The methods covered in this book include modeling and simulation, computation, analysis, control, optimization, data science, and machine learning. The engineering application topics include but are not limited to environmental engineering, cybersecurity, transportation, agriculture, smart grid, and next-generation manufacturing.

Phoronomics --- mechanics --- kinetics --- kinematics --- direction cosines --- Euler angles --- space dynamics --- digital computation --- control systems --- control engineering --- industrial cyber-physical systems --- cyber-attacks --- neural network --- model predictive control --- nonlinear chemical processes --- network classification --- network evolution --- network symmetries --- Green’s symmetry problem --- network invariants --- network internal dynamics --- symmetry ensembles --- propensities --- energy --- opening capability --- security --- smart grid --- group signature --- anonymous signature --- autonomous vehicle --- target detection --- multi-sensors --- fusion --- YOLO --- linear response eigenvalue problem --- block methods --- weighted Golub-Kahan-Lanczos algorithm --- convergence analysis --- thick restart --- mining vibrating screen --- theoretical rigid body model --- spring failures diagnosis --- amplitudes change --- real-time optimization --- nonlinear processes --- process control --- chemical reactor control --- distillation column control --- energy-based control --- payload swing attenuation --- linear matrix inequalities --- quadrotor --- larger Lipschitz constants --- comparative advantage --- transaction cost --- specialized production --- infra-marginal model --- agricultural division of labor --- velocity-slip --- temperature-jump --- homotopy analysis method --- nanofluids --- power-law fluids --- state estimation --- parameter estimation --- moving horizon estimation --- extended kalman filter --- ensemble kalman filter --- richards equation --- agro-hydrological systems --- economic model predictive control --- chemical processes --- responsive control --- artificial intelligence --- interpretability --- controller verification --- seashore soft soil --- cement --- sulfuric acid erosion --- stress–strain behavior --- mathematical model --- Micro Grid --- optimization theory --- optimization --- MATLAB simulation

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In recent years, various families of fractional-order integral and derivative operators, such as those named after Riemann-Liouville, Weyl, Hadamard, Grunwald-Letnikov, Riesz, Erdelyi-Kober, Liouville-Caputo, and so on, have been found to be remarkably important and fruitful, due mainly to their demonstrated applications in numerous seemingly diverse and widespread areas of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide interesting, potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables. For this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional-order integral and derivative operators and their multidisciplinary applications.

Legendre wavelet --- operational matrix --- systems of fractional order differential equations --- Liouville_Caputo sense --- analytic functions --- starlike functions --- univalent functions --- length problems --- SIR model --- Hermite collocation method --- approximate solution --- Hermite polynomials and series --- collocation points --- starlike and q-starlike functions --- q-derivative operator --- q-hypergeometric functions --- conic and generalized conic domains --- Hankel determinant --- Toeplitz matrices --- fractional differential equations --- Riemann-stieltjes integral --- monotone iterative method --- upper and lower solutions --- fractional diffusion equation --- controllability --- impulsive system --- unique continuation property --- non-linear fractional variational problems --- orthogonal polynomials --- Rayleigh-Ritz method --- error analysis --- convergence analysis --- Banach space --- Sobolev space --- Laplace operators --- nonlocal boundary conditions --- fractional differential systems --- mixed Riemann–Liouville integral --- mixed Hadamard integral --- Hilfer derivative --- Hadamard derivative --- coupled system --- random solution --- variable order fractional derivative --- initial value problem --- piecewise constant functions --- starlike function --- Toeplitz determinant --- sine function --- upper bound --- convex functions --- subordination --- logarithmic coefficients --- Gauss hypergeometric function --- confluent hypergeometric function --- Appell’s functions --- incomplete fractional calculus --- Riemann-Liouville fractional integral --- generating functions --- fractional integrals --- fractional derivatives --- Mittag–Leffler functions --- field spectrum --- fractional calculus --- desert soil --- available potassium --- correlation analysis --- Post-Exposure Prophylaxis --- latent reservoir --- HIV infection --- fractional order model --- multivalent functions --- close-to-convex functions --- uniformly starlike functions --- uniformly close-to-convex functions --- conic domains --- q-calculus --- differential subordination --- Janowski function --- cardioid domain --- limacon domain --- fractional order unknown input fuzzy observer --- fractional order Takagi–Sugeno models --- L2 optimization --- linear matrix inequalities --- unmeasurable premise variables --- global solutions --- fractional in time and space shallow-water system --- ψ-Caputo fractional derivative --- Hilfer fractional derivative --- Ulam stability --- pantograph differential equation --- nonlocal integral condition --- Miura transform --- soliton equations --- logarithm --- n/a --- mixed Riemann-Liouville integral --- Appell's functions --- Mittag-Leffler functions --- fractional order Takagi-Sugeno models