Special functions and analysis of differential equations /
edited by Praveen Agarwal, Ravi P. Agarwal, Michael Ruzhansky.
- First edition.
- 1 online resource (xv, 354 pages)
PrefaceEditorsContributors1 A Chebyshev Spatial Discretization Method for Solving Fractional Fokker-Planck Equation with Riesz DerivativesArman Dabiri, Behrouz Parsa Moghadam, and J. A. Tenreiro Machado2 Special Functions and Their Link with Nonlinear Rod TheoryGiovanni Mingari Scarpello and Daniele Ritelli3 Second Kind Chebyshev Wavelets for Solving the Variable-Order Space-Time Fractional Telegraph EquationMohammad Hossein Heydari, Ali Shakiba, Zakieh Avazzadeh, and Carlo Cattani4 Hyers-Ulam-Rassias Stabilities of Some Classes of Fractional Differential EquationsJ. E. Restrepo, R. A. Higuita, and Shilpi Jain5 Applications of Fractional Derivatives to Heat Transfer in Channel Flow of NanofluidsMuhammad Saqib, Ilyas Khan, and Sharidan Shafie6 The Hyperbolic Maximum Principle Approach to the Construction of Generalized ConvolutionsRúben Sousa, Manuel Guerra, and Semyon Yakubovich7 Elements of Aomoto's Generalized Hypergeometric Functions and a Novel Perspective on Gauss' Hypergeometric Differential EquationYasuhiro Abe8 Around Boundary Functions of the Right Half-Plane and the Unit DiscF.-H. Li and Shigeru Kanemitsu9 The Stankovich Integral Transform and Its ApplicationsArsen Pskhu10 Electric Current as a Continuous FlowYusuke Kamata, Tingli Ma, Yong Sun, and Shigeru Kanemitsu11 On New Integral Inequalities Involving Generalized Fractional Integral OperatorsM. Emin Özdemir, Ahmet Ocak Akdemir, Erhan Set, and Alper Ekinci12 A Note on Fox's H Function in the Light of Braaksma's ResultsDmitrii B. Karp13 Categories and Zeta & Möbius Functions: Applications to Universal Fractional OperatorsPhilippe Riot, Alain Le Méhauté, and Dmitrii Tayurskii14 New Contour Surfaces to the (2+1)-Dimensional Boussinesq Dynamical EquationHaci Mehmet Baskonus, Carlo Cattani, and Armando Ciancio15 Statistical Approach of Mixed Convective Flow of Third-Grade Fluid towards an Exponentially Stretching Surface with Convective Boundary ConditionAnum Shafiq, Zakia Hammouch, Tabassum Naz Sindhu, and Dumitru Baleanu16 Solvability of the Boundary-Value Problem for a Third-Order Linear Loaded Differential Equation with the Caputo Fractional DerivativePraveen Agarwal, Umida Baltaeva, and Jessada Tariboon17 Chaotic Systems and Synchronization Involving Fractional Conformable Operators of the Riemann-Liouville TypeJ. E. Solís-Perez, J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, and J. Reyes-ReyesIndex
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.