# Special Functions and Analysis of Differential Equations

DOI link for Special Functions and Analysis of Differential Equations

Special Functions and Analysis of Differential Equations book

# Special Functions and Analysis of Differential Equations

DOI link for Special Functions and Analysis of Differential Equations

Special Functions and Analysis of Differential Equations book

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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.

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

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

Chapter 2: Exact curvature’s effects on the redundant reactions: the case of a Euler-Bernoulli heavy cantilever

*Giovanni Mingari Scarpello, Daniele Ritelli*

Chapter 3: Second kind Chebyshev wavelets for solving variable-order space-time fractional telegraph equation

*M. H. Heydari, A.Shakiba, Z. Avazzadeh, C. Cattani*

Chapter 4: Hyers-Ulam And Hyers-Ulam-Rassias Stability For A Class Of Fractional Integro-Differential Equations

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

Chapter 5: Applications of Fractional Derivatives to Heat Transfer in Channel Flow of CMC Based CNTs Nanofluid

*Muhammad Saqib, Ilyas Khan, Sharidan Shafie*

Chapter 6: The hyperbolic maximum principle approach to the construction of generalized convolutions

*R´uben Sousa, Manuel Guerra, Semyon Yakubovich*

Chapter 7: Elements of Aomoto’s generalized hypergeometric functions and a novel perspective on Gauss’ hypergeometric differential equation

*Yasuhiro Abe*

Chapter 8: Around boundary functions of the right half-plane and the unit disc

*F.-H. Li, S. Kanemitsu*

Chapter 9: On the B. Stankovich integral transforms

*Arsen Pskhu*

Chapter 10 Electric current as a continuous flow

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

Chapter 11: On New Integral Inequalities Involving Generalized Fractional Integral Operators

*M. Emin Özdemir, Ahmet Ocak Akdemir, Erhan Set, Alper Ekinci*

Chapter 12: A note on Fox's H function in the light of Braaksma's results

*D.B. Karp*

Chapter 13: Fractional Dynamics, Riemann Zeta Functions and Self-Similarity, through Category Theory

*Philippe Riot, Alain Le Méhauté, Dmitrii Tayurskii*

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

*Haci Mehmet Baskonus, Carlo Cattani, Armando Ciancio*

Chapter 15: Statistical approch of mixed convective flow of third grade fluid towards an exponentially stretching surface with convective boundary condition

*Anum Shafiqa, Zakia Hammouch, Tabassum Naz Sindhu, Dumitru Baleanu*

Chapter 16: Solvability of the boundary-value problem for a third-order linear loaded differential equation with the Caputo fractional derivative

*Praveen Agarwal, Umida Baltaeva, Jessada Tariboon*

Chapter 17: Chaotic systems and synchronization involving fractional conformable operators of Riemann-Liouville type

*J.E. Sol´ıs-P´ereza**, J.F. G´omez-Aguilar, R.F. Escobar-Jim´enez, J. Reyes-Reyes*