This book "Advanced Applications of Computational Mathematics" covers multidisciplinary studies containing advanced research in the field of computational and applied mathematics. The book includes research methodology, techniques, applications, and algorithms. The book will be very useful to advanced students, researchers and practitioners who are involved in the areas of computational and applied mathematics and engineering.

Methods of Mathematical Modeling: Infectious Diseases presents computational methods related to biological systems and their numerical treatment via mathematical tools and techniques. Edited by renowned experts in the field, Dr. Hari Mohan Srivastava, Dr. Dumitru Baleanu, and Dr. Harendra Singh, the book examines advanced numerical methods to provide global solutions for biological models. These results are important for medical professionals, biomedical engineers, mathematicians, scientists and researchers working on biological models with real-life applications. The authors deal with methods as well as applications, including stability analysis of biological models, bifurcation scenarios, chaotic dynamics, and non-linear differential equations arising in biology. The book focuses primarily on infectious disease modeling and computational modeling of other real-world medical issues, including COVID-19, smoking, cancer and diabetes. The book provides the solution of these models so as to provide actual remedies.

This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus.
The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering.
Some of the areas of present-day applications of fractional models include Fluid Flow, Solute Transport or Dynamical Processes in Self-Similar and Porous Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on.
In the above-mentioned areas, there are phenomena with estrange kinetics which have a microscopic complex behaviour, and their macroscopic dynamics can not be characterized by classical derivative models.
The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order, that is, we can speak about a derivative of order 1/3, or square root of 2, and so on. Some of such fractional models can have solutions which are non-differentiable but continuous functions, such as Weierstrass type functions. Such kinds of properties are, obviously, impossible for the ordinary models.
What are the useful properties of these fractional operators which help in the modelling of so many anomalous processes? From the point of view of the authors and from known experimental results, most of the processes associated with complex systems have non-local dynamics involving long-memory in time, and the fractional integral and fractional derivative operators do have some of those characteristics.
This book is written primarily for the graduate students and researchers in many different disciplines in the mathematical, physical, engineering and so many others sciences, who are interested not only in learning about the various mathematical tools and techniques used in the theory and widespread applications of fractional differential equations, but also in further investigations which emerge naturally from (or which are motivated substantially by) the physical situations modelled mathematically in the book.
This monograph consists of a total of eight chapters and a very extensive bibliography. The main objective of it is to complement the contents of the other books dedicated to the study and the applications of fractional differential equations. The aim of the book is to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy type problems involving nonlinear ordinary fractional differential equations, explicit solutions of linear differential equations and of the corresponding initial-value problems through different methods, closed-form solutions of ordinary and partial differential equations, and a theory of the so-called sequential linear fractional differential equations including a generalization of the classical Frobenius method, and also to include an interesting set of applications of the developed theory.
Key features:
- It is mainly application oriented.
- It contains a complete theory of Fractional Differential Equations.
- It can be used as a postgraduate-level textbook in many different disciplines within science and engineering.
- It contains an up-to-date bibliography.
- It provides problems and directions for further investigations.
- Fractional Modelling is an emergent tool with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering.
- It contains many examples.
- and so on

Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms.