Differential Equations are very important tools in Mathematical
Analysis. They are widely found in mathematics itself and in its
applications to statistics, computing, electrical circuit analysis,
dynamical systems, economics, biology, and so on. Recently there
has been an increasing interest in and widely-extended use of
differential equations and systems of fractional order (that is, of
arbitrary order) as better models of phenomena in various physics,
engineering, automatization, biology and biomedicine, chemistry,
earth science, economics, nature, and so on. Now, new unified
presentation and extensive development of special functions
associated with fractional calculus are necessary tools, being
related to the theory of differentiation and integration of
arbitrary order (i.e., fractional calculus) and to the fractional
order (or multi-order) differential and integral equations. This
book provides learners with the opportunity to develop an
understanding of advancements of special functions and the skills
needed to apply advanced mathematical techniques to solve complex
differential equations and Partial Differential Equations (PDEs).
Subject matters should be strongly related to special functions
involving mathematical analysis and its numerous applications. The
main objective of this book is to highlight the importance of
fundamental results and techniques of the theory of complex
analysis for differential equations and PDEs and emphasizes
articles devoted to the mathematical treatment of questions arising
in physics, chemistry, biology, and engineering, particularly those
that stress analytical aspects and novel problems and their
solutions. Specific topics include but are not limited to Partial
differential equations Least squares on first-order system Sequence
and series in functional analysis Special functions related to
fractional (non-integer) order control systems and equations
Various special functions related to generalized fractional
calculus Operational method in fractional calculus Functional
analysis and operator theory Mathematical physics Applications of
numerical analysis and applied mathematics Computational
mathematics Mathematical modeling This book provides the recent
developments in special functions and differential equations and
publishes high-quality, peer-reviewed book chapters in the area of
nonlinear analysis, ordinary differential equations, partial
differential equations, and related applications.
General
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