Živorad Tomovski, picture is taken from the webpage.
Zivorad Tomovski is NEWFELPRO's researcher in incoming scheme, who arrived from the Faculty of Natural Sciences and Mathematics (University of Skopje) to the Department of Mathematics at the University of Rijeka
to perform his research on a project titled Modeling anomalous diffusion by generalized Langeven, Fokker-Planck equations and fractional diffusion-wave equations
(Anomalous diffusion) under the mentorship of dr. Bojan Crnković
Professor Tomovski‘s project is aimed at reviewing some partial differential equations that are at the center of interest in modern physics. Recent advances in the fractional differential equations stimulated new examples of applications in fluid mechanics, viscoelasticity, electromagnetism, hydrology, mathematical biology, electrochemistry, robotics, signal processing, turbulence and many other problems. Fractional differential equations are useful tools for modeling many unusual phenomena in nature and theory of complex systems. The main objective of adoption and research diffusion equation fractional order is to describe the phenomenon of unnatural diffusion which is commonly encountered in transport processes of complex and / or disordered systems, including fractal media.
On the basis of this project are issued or under preparation following scientific papers:
• Published papers:
"Generalized Opial––type inequalities for differential and integral operators with special kernels in fractional calculus.“ (coauthors: J.Pecarić and G.Farid).
„Some families of Mathieu type series and Hurwitz-Lerch zeta functions and associated probability distributions“, Applied and Computational Mathematics, vol. 14, No. 3, (2015) (coauthors: Hari M. Srivastava and Delco Leskovškova ).
"Opial- type inequalities for fractional integral operators involving Mittag-Leffler functions" Fractional Differential Calculus, Vol (5) (2015) (1), 93-106 (coauthors: J.Pecaric i G. Farid).
"Analytical solution of generalized space-time fractional cable equation", Mathematics 2015, 3, 153-170 (coauthors: R.K.Saxena i T. Sandev).
"Space-time fractional Schrodinger equation with composite time fractional derivative", Fractional Calculus and Applied Analysis Vol. 18 (5) (2015) (coauthors:Johan Dubbeldam i T. Sandev)
„Some properties of Prabhakar fractional calculus operators“ Fractional Differential Calculus , Vol. 6 (1) (2016), 73-94 (coauthor Federic Polito).
Papers in in writing phase.:
„Stochastic representation of generalized distributed order wave equation“ (coauthor: Trifce Sandev).
„Anomalous diffusion processes“ (coauthor: dr. Trifce Sandev).
In the phase of soon publication:
„Generalized distributed order diffusion equations with composite fractional derivative“ (u suradnji s Trifce Sandevom i Bojanom Crnkovićem), Computers and Mathematics with Applications (u suradnji s Trifce Sandevom i Bojanom Crnkovićem).
„Weighted Opial nequalities for fractional integral and differential operators involving generalized Mittag-Leffler functions“ , European J. Pure Applied Mathematics, (u suradnji s J.Pecarićem i G.Faridom).
„Hardy type inequalities for generalized fractional integral operators“, (Tbilisi Math. Journal) (u suradnji sa Sajid Iqbalom, Josipom Pecaricem i Muhammadom Samraizem).
During the implementation of his NEWFELPRO project he held a lecture "Complete monotonicity of the MIttag-Leffler functions and opial type inequalities" at the seminar in organisation of the Department of Statistics at the University of Rome.
This is the fifth international research scholarship for Professor Tomovski, and the second one in Croatia. As of yet, he was the manager of the five research projects:
•(2001-2004) Fourier Analysis and Applications (supported by Ministry of Sciences of Macedonia).
•(2006-2009) Nontrigonometric Fourier Analysis, and Special Orthogonal Functions and Applications (supported by Ministry of Education and Sciences of Macedonia).
•(2006-2008) Fractional Calculus, Higher Transcedential Functions and Applications (Bilaterial Project supported by Ministry of Education and Sciences of Macedonia and Ministry of Science and Sport of Croatia).
•(2008) Fractional and Operational Calculus with Mittag-Leffler type functions (supported by DAAD Foundation-Germany).
•(2011) Linear and Nonlinear Fractional Models with Applications to Diffusion Processes (supported by DAAD Foundation-Germany)
•(2011) Modeling of physical processes by generalized Langevin equations and space-time fractional diffusion-wave equations (supported by NWO grant, The Netherlands)
•(2011-2013) Linear and Nonlinear Fractional Diffusion Models (Bilaterial Project between Macedonia and Austria)
Professor Tomorovski is a reviewer for a number of reputable scientific journals, a professional member of the Research Group Mathematical Inequalities & Applications (Melbourne, Australia) since 1999, and a member of the Humboldt and DAAD Club since 2008. After the implementation of his NEWFELPRO project, further wishes and future plans of Professor Tomovski are to continue his career as a university professor at one of the universities in Republic of Croatia.