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"Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, and other scientists an elementary level explanation of integral equations of the first kind. It maintains a casual, conversational approach. The book emphasizes understanding, while deliberately avoiding special methods of highly limited application."

"This book offers a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. Includes nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts. Included in the presentation are, a section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter, thorough discussions of the analytical methods used to solve many types of integral equations, an introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations, over 80 illustrative examples that are explained in meticulous detail, nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts, and guides to computation to assist the student with particularly complicated algorithmic procedures."

"Introduces a rigorous investigation of q-difference operators in standard and fractional settings. This monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi."

"This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data.This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poissons and Naviers equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization."

"Topics in fractional differential equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. ​​Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena, in particular the modeling of memory-dependent and complex media such as porous media. "