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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.

gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion

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• Reference Manager
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• RefWorks (Direct export to RefWorks)

This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.

Research & information: general --- Mathematics & science --- gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion --- gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion

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During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of fractional differential equations.

weakly upper semicontinuous --- essential maps --- homotopy --- Riemann-Liouville fractional differential equation --- delay --- lower and upper solutions --- monotone-iterative technique --- homoclinic solutions --- fourth-order p-Laplacian differential equations --- minimization theorem --- Clark’s theorem --- exponential dichotomy --- roughness --- asymptotically constant matrices --- double fuzzy Sumudu transform --- partial Volterra fuzzy integro-differential equations --- n-th order fuzzy partial H-derivative --- m-dissipative operators --- limit solutions --- integral solutions --- one-sided Perron condition --- Banach spaces --- fixed point --- complete metric space --- fractional differential equations --- optimal feedback control --- Voigt model --- alpha-model --- fractional derivative --- Riemann–Liouville fractional differential equations --- nonlocal boundary conditions --- positive solutions --- existence --- multiplicity --- Caputo derivative --- Riemann–Liouville integral --- multipoint and sub-strip boundary conditions --- fixed point theorem --- fractional Navier–Stokes equations --- variable delay --- modified fractional Halanay inequality --- generalized comparison principle --- dissipativity --- Fourier-Laplace transforms --- porous material --- eigenvalues method --- fractional time derivative

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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

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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.

Research & information: general --- Mathematics & science --- 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 --- 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