Special Functions and Analysis of Differential Equations

Differential Equations are very important tool in Mathematical Analysis. These 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 of 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 PDE's problems. 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 PDE's, 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 provide the recent developments in Special functions and Differential Equations and publishing high quality peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations and related applications.