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 problemsList of Chapters1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation3. Incomplete K2-Function4. Some Results On Incomplete Hypergeometric Functions5. Transcendental Bernstein Interpolation and Approximation6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function7. From Abel continuity theorem to Paley-Wiener theorem...8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion11. General fractional order quadratic functional integral Existence, properties of solutions and some of its Applications12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes Existence of solutions, continuous dependence and applications13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions15. On solutions of Kinetic Model by Sumudu transform