Recent Developments in Theory and Applications of Fractional Order Systems

Dr. Mehmet Yavuz received his Ph.D. degree in Applied Mathematics from Balikesir University, Turkey. He conducted postdoctoral research in the Department of Mathematics at the University of Exeter, U.K., in 2019-2020. He is currently an Associate Professor in the Mathematics and Computer Sciences Department at Necmettin Erbakan University, Turkey. He has published more than 70 research papers in reputed journals and 60 conference papers as well as 6 book chapters in international books. He is the Editor of Fractional Calculus: New Applications in Understanding Nonlinear Phenomena, Bentham Books. His research interests include fractional calculus and its applications to the different fields of science, mathematical biology, nonlinear dynamics, and optimal control. Apart from being an Associate Editor of several esteemed journals, he is the Editor-in-Chief of Mathematical Modelling and Numerical Simulation with Applications. Dr. Dharmendra Kumar Singh is an Assistant Professor in the Department of Mathematics, School of Basic Sciences, UIET, Chhatrapati Sahau Ji Maharaja University, Kanpur, India. His research interest is in Special functions, fractional calculus, partial fractional differential equations, and distribution theory. Dr. Singh received the A.K. Agarwal prize for best publication from The Society for Special Functions and Their Applications. Dr. Stuart Townley is particularly interested research involving dynamical systems and control: the study of things (mechanical, biological, electrical, etc.) which interact and evolve in time and can be predicted, managed, and optimized. Dr. Townley has been the Chair in Applied Mathematics at the Environment and Sustainability Institute of the University of Exeter since June 2011. He works closely with colleagues in the College of Engineering, Mathematics and Physical Sciences, as well as in the College of Life and Environmental Sciences, to understand natural and man-made systems. Dr. Townley is also a member of the Mathematics Department in the College of Engineering, Mathematics and Physical Sciences, University of Exeter. He has previously held the positions of Chair in Applied Mathematics, Head of Department in the School of Mathematics, and Associate Dean in the Postgraduate Faculty at the University of Exeter.

• 1. Special Functions of the Fractional Calculus2. Fractional Derivatives and Integrals3. Transforms of Fractional Derivatives4. Linear Fractional Differential Equations5. Fractional Green's Function6. Other Methods for the Solution of Fractional-order Equations7. Fractional ordinary differential equations and properties8. Existence and uniqueness of solutions to Cauchy-type problems9. Stability estimates for fractional order differential equations10. Partial Fractional differential equations and their solutions11. Numerical Evaluation of Fractional Derivative12. Approximation of Fractional Derivatives13. Numerical method for fractional order ordinary differential equations14. Finite-difference method for fractional ODEs15. High-order approximation of Caputo fractional derivative16. Adaptive and high-order scheme for non-integer order differential equations17. Time-fractional diffusion equations18. Fractional diffusion19. Fractional‐order Modeling20. Linear Fractional‐order Systems21. Current trends in fractional derivatives22. Fractional‐order Control23. Fractional integral inequalities and Applications24. Discrete fractional calculus and applications25. Fractional variational calculus and fractional Euler-Lagrange Equation26. Fractional Calculus in Image/Signal Processing