## ABSTRACT

Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on.

This Handbook:

- Provides reliable methods for solving fractional-order models in science and engineering.
- Contains efficient numerical methods and algorithms for engineering-related equations.
- Contains comparison of various methods for accuracy and validity.
- Demonstrates the applicability of fractional calculus in science and engineering.
- Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations.

Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.

1. Analytical and Numerical Methods to Solve the Fractional Model of the Vibration Equation

2. Analysis of a Nonlinear System Arising in a Helium-Burning Network with Mittag–Leffler Law

3. Computational Study of Constant and Variable Coefficients Time-Fractional PDEs via Reproducing Kernel Hilbert Space Method

4. Spectral Collocation Method Based Upon Special Functions for Fractional Partial Differential Equations

5. On the Wave Properties of the Conformable Generalized Bogoyavlensky–Konopelchenko Equation

6. Analytical Solution of a Time-Fractional Damped Gardner Equation Arising from a Collisional Effect on Dust-ion-Acoustic* ***Waves in a Dusty Plasma with Bi-Maxwellian Electrons**

7. An Efficient Numerical Algorithm for Fractional Differential Equations

8. Generalization of Fractional Kinetic Equations Containing Incomplete *I*-Functions

9. Behavior of Slip Effects on Oscillating Flows of Fractional Second-Grade Fluid

10. A Novel Fractional-Order System Described by the Caputo Derivative, Its Numerical Discretization, and Qualitative Properties

11. Extraction of Deeper Properties of the Conformable Gross–Pitaevskii Equation via Two Powerful Approaches

12. New Fractional Integrals and Derivatives Results for the Generalized Mathieu-Type and Alternating Mathieu-Type Series