# Special Functions and Analysis of Differential Equations

Praveen Agarwal (Redaktør) ; Ravi P Agarwal (Redaktør) ; Michael Ruzhansky (Redaktør)

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**2363,-**

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Leveringstid: Sendes innen 21 dager

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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.

Editors

Contributors

1 A Chebyshev Spatial Discretization Method for Solving Fractional Fokker-Planck Equation with Riesz Derivatives

Arman Dabiri, Behrouz Parsa Moghadam, and J. A. Tenreiro Machado

2 Special Functions and Their Link with Nonlinear Rod Theory

Giovanni Mingari Scarpello and Daniele Ritelli

3 Second Kind Chebyshev Wavelets for Solving the Variable-Order Space-Time Fractional Telegraph Equation

Mohammad Hossein Heydari, Ali Shakiba, Zakieh Avazzadeh, and Carlo Cattani

4 Hyers-Ulam-Rassias Stabilities of Some Classes of Fractional Differential Equations

J. E. Restrepo, R. A. Higuita, and Shilpi Jain

5 Applications of Fractional Derivatives to Heat Transfer in Channel Flow of Nanofluids

Muhammad Saqib, Ilyas Khan, and Sharidan Shafie

6 The Hyperbolic Maximum Principle Approach to the Construction of Generalized Convolutions

Ruben Sousa, Manuel Guerra, and Semyon Yakubovich

7 Elements of Aomoto's Generalized Hypergeometric Functions and a Novel Perspective on Gauss' Hypergeometric Differential Equation

Yasuhiro Abe

8 Around Boundary Functions of the Right Half-Plane and the Unit Disc

F.-H. Li and Shigeru Kanemitsu

9 The Stankovich Integral Transform and Its Applications

Arsen Pskhu

10 Electric Current as a Continuous Flow

Yusuke Kamata, Tingli Ma, Yong Sun, and Shigeru Kanemitsu

11 On New Integral Inequalities Involving Generalized Fractional Integral Operators

M. Emin OEzdemir, Ahmet Ocak Akdemir, Erhan Set, and Alper Ekinci

12 A Note on Fox's H Function in the Light of Braaksma's Results

Dmitrii B. Karp

13 Categories and Zeta & Moebius Functions: Applications to Universal Fractional Operators

Philippe Riot, Alain Le Mehaute, and Dmitrii Tayurskii

14 New Contour Surfaces to the (2+1)-Dimensional Boussinesq Dynamical Equation

Haci Mehmet Baskonus, Carlo Cattani, and Armando Ciancio

15 Statistical Approach of Mixed Convective Flow of Third-Grade Fluid towards an Exponentially Stretching Surface with Convective Boundary Condition

Anum Shafiq, Zakia Hammouch, Tabassum Naz Sindhu, and Dumitru Baleanu

16 Solvability of the Boundary-Value Problem for a Third-Order Linear Loaded Differential Equation with the Caputo Fractional Derivative

Praveen Agarwal, Umida Baltaeva, and Jessada Tariboon

17 Chaotic Systems and Synchronization Involving Fractional Conformable Operators of the Riemann-Liouville Type

J. E. Solis-Perez, J. F. Gomez-Aguilar, R. F. Escobar-Jimenez, and J. Reyes-Reyes

Index

Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology, Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His research interests include numerical analysis, inequalities, fixed point theorems, and differential and difference equations. He is the author/co-author of over 1000 journal articles and more than 25 books, and actively contributes to over 500 journals and book series in various capacities.

Michael Ruzhansky is a professor at the Department of Mathematics, Imperial College London. He has published over 100 research articles in several leading international journals. He has also published five books and memoirs and nine edited volumes. He has researched topics related to pseudo-differential operators, harmonic analysis and partial differential equations. More recently, he has worked on boundary value problems and their applications. He has been on the editorial board of many respected international journals and served as the President of the International Society of Analysis, Applications, and Computations (ISAAC) in the period 2009-2013.