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The topics of special H-function and fractional calculus are currently undergoing rapid changes both in theory and application. Taking into account the latest research results, the authors delve into these topics as they relate to applications to problems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics. The book sets forth the definitions, contours, existence conditions, and particular cases for the H-function, then explores the properties and relationships among the Laplace, Fourier, Hankel, and other transforms. From here, the H-functions are utilized for applications in statistical distribution theory, structures of random variables, generalized distributions, Mathai’s pathway models, and versatile integrals. Functions of matrix argument are introduced with a focus on real-valued scalar functions when the matrices are real or Hermitian positive-definite. The text concludes with important recent applications to physical problems in reaction, diffusion, reaction-diffusion theory and statistics, and superstatistics. Generalized entropies as well as applications in astrophysics are dealt with. Over the last few years, material in this book has been added to various courses and developed to meet the needs of scholars at the PhD level. All exercises in the book have been used to probe the knowledge and ability of mathematics, statistics, and physics to students and researchers. .

H-functions. --- H-functions --- Calculus --- Physics - General --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Hypergeometric functions. --- Functions, Hypergeometric --- Fox's H-function --- G-functions, Generalized --- Generalized G-functions --- Generalized Mellin-Barnes functions --- Mellin-Barnes functions, Generalized --- Physics. --- Functional analysis. --- Special functions. --- Statistics. --- Applied mathematics. --- Engineering mathematics. --- Theoretical, Mathematical and Computational Physics. --- Functional Analysis. --- Mathematical Methods in Physics. --- Special Functions. --- Statistical Theory and Methods. --- Appl.Mathematics/Computational Methods of Engineering. --- Transcendental functions --- Hypergeometric series --- Hypergeometric functions --- Mathematical physics. --- Functions, special. --- Mathematical statistics. --- Mathematical and Computational Engineering. --- Physical mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Engineering --- Engineering analysis --- Mathematical analysis --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Special functions --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematical and Computational Engineering Applications. --- Data processing.