In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties.
This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. Interesting applications of special functions and partial differential equations are demonstrated by 15 chapters. Many chapters highlight the importance of numerical techniques and the results of complex analysis. Contributions in the book emphasize the mathematical treatment of questions arising in natural sciences and engineering, particularly those that involve novel problems and their solutions.
This volume is a timely update for mathematicians and researchers interested in advanced numerical methods and computational techniques used to solve complex problems
List of Chapters
1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters
2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation
3. Incomplete K2-Function
4. Some Results On Incomplete Hypergeometric Functions
5. Transcendental Bernstein Series: Interpolation and Approximation
6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function
7. From Abel continuity theorem to Paley-Wiener theorem…
8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials
9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations
10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion
11. General fractional order quadratic functional integral equations: Existence, properties of solutions and some of its Applications
12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes type: Existence of solutions, continuous dependence and applications
13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions
14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions
15. On solutions of Kinetic Model by Sumudu transform
Table of Contents
Chapter 1 General Fractional Order Quadratic Functional Integral Equations: Existence, Properties of Solutions, and Some of Their Applications
- Introduction
2. Preliminaries
3. Existence of Solutions
3.1. Carathéodory Theorem for the Quadratic Integral Equation (1)
4. Special Cases and Remarks
5. Properties of Solutions.
5.1. Uniqueness of Solutions of Qfie (1)
5.2. Maximal and Minimal Solutions
5.3. Comparison Theorem
5.4. 𝜹−Approximate Solutions..............
6. Applications.
6.1. Hybrid Functional 𝝓−Differential Equation of Fractional Order
6.2. Pantograph Functional 𝝓−Differential Equation of Fractional Order.........................
- Conclusion........
- Consent for Publication
- Conflict of Interest
- Acknowledgements
- References
Chapter 12 Non-Linear Set-Valued Delay Functional Integral Equations of Volterrastieltjes Type: Existence of Solutions, Continuous Dependence and Applications…………………………………………………………………………………………………………… 219 A. M. A. El-Sayed, Sh. M Al-Issa and Y. M. Y. Omar 1.
- Introduction
2. Preliminaries
3. Single-Valued Problem..............
3.1. Existence of Solutions I
4. Uniqueness of the Solution
4.1. Continuous Dependence of the Solution
4.1.1. Continuous Dependence on the Delay Functions (𝒕)................................................
4.1.2. Continuous Dependence on the Functions (𝒕,𝒔)
4.2. Application 1
5. Existence of Solutions Ii
5.1. Application 2
6. Set-Valued Problem
6.1. Existence of Solution
6.2. Continuous Dependence on the Set of Selection 𝑺𝑭𝟏
6.3. Set-Valued Chandrasekhar Non-Linear Quadratic Functional Integral Inclusion
6.4. Volterra Integral Inclusion of Fractional Order
6.4.1. Differential Inclusion
- Conclusion........
- Consent for Publication
- Conflict of Interest
- Acknowledgements
- References
Chapter 13 Certain Saigo Fractional Derivatives of Extended Hypergeometric Functions
Author
- Praveen Agarwal
-Shilpi Jain
