Fractional Order Analysis Theory, Methods and Applications

The book contains new research findings in fractional order analysis. Different tools and techniques from the field of fractional order analysis are found to be extremely helpful in practical applications because such analyses can help in developing mathematical methods or models more accurately. The book covers topics such as: conformable fractional operators, local fractional proportional derivatives, fractional derivative and integral operators, different inequalities via several fractional environments, different type of fractional integral operators, fractional-order chaotic model, flow models in fractional environment, multi-dimensional fractional order models, fractional modelling of the transmission dynamics of Influenza, and Zika virus model with various fractional derivatives. Using this book, readers can find several useful, relevant and connected topics in one place, which is necessary for crucial understanding of research problems of an applied nature.

This book can be a reference for courses in Mathematical Analysis at undergraduate and postgraduate levels. Additionally, this book could be used in specialized courses (1/2 weeks to 6 months duration) usually offered by mathematical societies/organizations, in university departments, and in research institutions on fractional calculus, fractional analysis, non-linear analysis, fractional dynamics, and nonlinear dynamics.

HEMEN DUTTA, PHD, is Faculty Member in the Department of Mathematics at Gauhati University, Guwahati, India.

AHMET OCAK AKDEMIR, PHD, is Associate Professor, Ağrı İbrahim Çeçen University, Faculty of Science and Letters, Department of Mathematics, Ağrı, Turkey.

ABDON ATANGANA, PHD, is Professor, Institute for Groundwater Studies, University of the Free State, Bloemfontein, South Africa.

1. On the fractional derivative and integral operators

2. Generalized conformable fractional operators and their applications

3. Analysis of new trends of fractional differential equations

4. New estimations for exponentially convexity via conformable fractional operators

5. Lyapunov type inequalities for local fractional proportional derivatives

6. Minkowski type inequalities for mixed conformable fractional integrals

7. New estimations for different kinds of convex functions via conformable integrals and Riemann-Liouville fractional integral operators

8. Legendre-Spectral Algorithms for Solving Some Fractional Differential Equations

9. Mathematical Modeling of an Autonomous Nonlinear Dynamical System for Malaria Transmission using Caputo Derivative

10. MHD free convection flow over a vertical plate with ramped wall temperature and chemical reaction in view of non-singular kernel

11. Comparison of the different fractional derivatives for the dynamics of Zika virus