Toka Diagana, Ph.D.
Department of Mathematics
Washington DC 20059
My personal web page
Ph. D. (1999) Université Claude Bernard - Lyon, France
Research Interests: Operator Theory; (p-adic) Functional Analysis ;
Abstract Differential Equations; Stochastic Differential Equations; Difference Equations; and Integrodifferential Equations.
Most interesting phenomena encountered in our daily life can be described through
differential equations. In recent years, my goal has been to
study the existence of solutions to abstract differential
equations in various classes of functions such as almost
periodic functions, almost automorphic functions, pseudo almost
periodic functions, pseudo almost automorphic functions as well
as weighted pseudo almost periodic functions we recently
introduced in the literature. One of my current goals consists
of studying singular and fractional differential equations in
connection with the above-mentioned classes of functions.
It is well-known that the best way to understand properties of linear
operators is through their spectral analysis. In particular, the spectral
theory for linear operators plays a crucial role in several fields
including quantum mechanics. Except for a few investigations such as the
pioneer work of Vishik, there is no general spectral theory for linear
operators in the non-archimedean setting. One of my current goals consists
of developing a general spectral theory for unbounded linear operators on
non-archimedean Banach spaces.
Almost automorphic type and almost periodic type functions in abstract spaces, Springer, New York, 2013
Almost Periodic Stochastic Processes, Springer, New York, 2011 (with P. H. Bezandry)
Pseudo Almost Periodic Functions in Banach Spaces, Nova Science Publishers, New York, 2007
- Existence of pseudo almost automorphic mild solutions to some nonautonomous second order differential equations. Rocky Mt. J. Math. 43 (2013), No. 3, 793-824.
- (with P. H. Bezandry) Square-Mean Almost Periodic Solutions to Some Classes of Nonautonomous Stochastic Evolution Equations With Finite Delay. J. Appl. Funct. Anal. 7 (2012), no. 4, 345--366.
- Existence of globally attracting almost automorphic solutions to some nonautonomous higher-order difference equations, Appl. Math. Comput. 219 (2013), no. 12, 6510--6519.
- Bounded solutions to some classes of nonautonomous higher-order differential equations. Afr. Mat. 24 (2013), No. 1, 33-53.
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients. Mathematica Slovaca. 2013. To appear.
- Almost automorphic solutions to some damped second-order differential equations. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 11, 4074--4084.
- Almost periodic solutions to some second-order nonautonomous differential equations. Proc. Amer. Math. Soc. 140 (2012), no. 1, 279--289.
- Pseudo-almost periodic solutions for some classes of nonautonomous partial evolutions equations. J. Franklin Inst. 348 (2011), no. 8, 2082 -- 2098.
- Almost periodic solutions for some higher-order nonautonomous differential equations with operator coefficients. Math. Comput. Modeling 54 (2011), no. 11-12, 2672 -- 2685.
- Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations. J. Math. Anal. Appl. 350 (2009), no. 1, 18--28.
- (with M. Baroun, S. Boulite, and L. Maniar), Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations. J. Math. Anal. Appl. 349 (2009), no. 1, 74--84.
- (with H. Henriquez and E. Hernandez), Asymptotically almost periodic solutions to some classes of second-order functional differential equations. Differential Integral Equations 21 (2008), no. 5-6, 575--600.
Associate Editor for the following mathematical journals:
- Abstract and Applied Analysis (AAA)
- Advances in Difference Equations (ADE)
- Advances in Differential Equations and Control Processes(ADECP)
- Advances in Theoretical and Applied Mathematics(ATAM)
- Afrika Matematika
- Involve: A Journal of Mathematics
- International Journal of Differential Equations(IJDE)
- Journal of Nonlinear Evolution Equations and Applications
- Journal of Mathematical Control Science and Applications
- International Journal of Statistika and Mathematika
Editor-in-Chief of the following mathematical journal:
- Nonautonomous and Stochastic Dynamical Systems
Founding (Managing) Editor for the following mathematical journals:
- Communications in Mathematical Analysis (CMA)
- Journal of Abstract Differential Equations and Applications (JADEA)
- African Diaspora Journal Of Mathematics (ADJM)