Professor, Mathematical Sciences
B.S., Math, Phy, Chem. Sri Satya Sai Institute of Higher Learning, Prasanthinilayam, India 1985
M.S., Mathematics Sri Satya Sai Institute of Higher Learning, Prasanthinilayam, India 1987
PhD. Thesis: A study of Mixed Linear Regular Ordinary Differential Operators Sri Sathya Sai Institute of Higher Learning, Prasanthinilayam, India 1990
Multi Variable Calculus, Differential Equations/Linear Algebra
2007- to Present, Professor, Florida Institute of Technology, Melbourne,FL.
2003-2007, Associate Professor, Florida Institute of Technology, Melbourne, USA
2002–2003, Visiting Associate Professor, Florida Institute of Technology, Melbourne, USA
1995–2002, Assistant Professor of Mathematics, Indian Institute of Technology, Delhi
1994Â–1995, Lecturer in Mathematics, IIT, Delhi
1992-1994, Research Associate, IIT, Kanpur
1990-1992, Lecturer, Sri Satya Sai Institute of Higher Learning, Prasanthinilayam, India
My main area of research is qualitative theory of linear/nonlinear differential equations. I have worked on fuzzy differential equations, set differential equations and functional differential equations. Recently, I have been studying some fundamental aspects of the functional differential equations with anticipation and retardation (FDEAR). These FDEAR are an important class of differential equations that have applications to signal analysis, biology and social sciences.
I am also interested in Wavelet Analysis and its applications to boundary value problems and to image processing problems.
Image inpainting, Phase Unwrapping for Synthetic Aperture Radar, and Radar image processing are some of the industrial applications that I study using the theory of differential equations and wavelet analysis.
I have the following joint patent aprroved by the United States Patent and Trademark Office (USPTO):
Sartor; Kenneth, Allen; Josef , Ganthier; Emile, Gilbert; Bernard S., Tenali; Gnana Bhaskar, Method and apparatus for processing complex interferometric SAR data;
Existence and uniqueness results for fuzzy linear differential-algebraic equations, Fuzzy Sets and Systems 245 (2014) 30–42 (with R. Alikhani, F. Bahrami)
Some results for impulsive problems via Morse theory, J. Math. Anal. Appl. 409 (2014) 752–759. (with R.P. Agarwal, Kanishka Perera)
On some elliptic interface problems with nonhomogeneous jump conditions, Advances in Nonlinear Analysis. 2(2), 195–211, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: 10.1515/anona-2013-0005, May 2013 (with Kanishka Perera)
New uniqueness results for fractional differential equations, Applicable Analysis, 92 (2), 2013, 259-269. (with Fulya Yoruk and R.P. Agarwal)
Oscillation results for second order nonlinear neutral delay dynamic equations, , Func. Diff. Eqns. 17 (3-4), (2010), 329 - 344. (with A. K. Tripathy )
Fractional Differential Equations with Krasnoselskii-Krien type condition, Nonlinear Analysis, Hybrid Systems 3 (2009) 734-737. (with V. Lakshmikantham and S Leela)
Revisiting the hybrid real number system, Nonlinear Analysis, Hybrid Systems 3 (2009) 101-107 (with E. Escultura, V. Lakshmikantham and S Leela)
Set Differential Equations in Frechet Spaces, J. Appl. Anal. 14 (1), 2008. (with Galanis, G. and V. Lakshmikantham)
Heatlet approach to diffusion equation on unbounded domains, Appl. Math. Comp. 197 (2008) 891- 903.(with Hariharan, S. and N. Nataraj)
Variational phase unwrapping and wavelet denoising of interferometric SAR data using Mumford-Shah framework, Int.J.Signal and Imaging Sys.Eng.
1(2),2008 ,145 - 152. (with K. Sartor and S. Kozaitis.
An existence theorem for set differential inclusions in a metric space, Control and Cybernatics, 36 (2007) (3), 571- 582. (with De Blasi, FS and V. Lakshmikantham)
Fixed Point Theorems in Partially ordered Metric Spaces and Applications, Nonlinear. Anal.Appl. TMA. 65, 2006, 1379-1393. (with V. Lakshmikantham)
Set valued functions in Frechet spaces: continuity, Hukukara differentiability and applications to set differential equations, Nonlinear Anal. TMA, 61 (4) 2005, 559-575. (with Galani, G., and V. Lakshmikantham)
Revisiting Fuzzy differential equations, Non.Anal.TMA 58 (2004), 351-358. (with V. Lakshmikantham and JV Devi).
Lyapunov Stability for Set Differential Equations. Dynamic Systems and Applications. 13(1), 2004, 1-10. (with V Lakshmikantham)
Proximal Normals and Flow Invariance for Differential Inclusions, Nonlinear Studies 10(1), 2003, 29-37. (with V. Lakshmikantham)
Set Differential equations and Flow Invariance, Applicable Analysis, 2003, 82(4), 357-368. (with V. Lakshmikantham)
Generalized proximal normals and Lyapunov Stability, Nonlinear Studies 10(4), 2003, 335-341. (with V. Lakshmikantham)
Comparison theorem for a nonlinear boundary value problem on time scales, J. Comp. and App. Math. (special issue on Dynamic Equations on Time Scales), 141, (1-2), 2002, 117-122.
Analyticity of semigroup generated by a class of differential operators with interface, Nonlinear Analysis, TMA 39 (2000) 779-791. (MR2000j:47075) (with Rajiv Kumar)