Muhammad Islam

Professor
Full-Time Faculty
College of Arts and Sciences: Mathematics

Profile

Professor Islam began his career at the University of Dayton in 1985 as a full time faculty member in mathematics. He teaches mathematics courses at all levels.

Faculty Perspective

My graduate education and subsequent research work in applied mathematics serve as the foundation of my strong interest in various applications of mathematics.  Over the years at the University of Dayton, I have been involved in many activities including developing applications that student can utilize in their future careers.

Degrees

  • Ph. D., Southern Illinois University at Carbondale, Carbondale, IL (1985)
  • M. Sc., Carleton University, Ottawa, Ontario, Canada (1980)

Research Interests

  • Qualitative analysis of ordinary and functional differential equations

Selected Publications

"Bounded, L^1, and asymptotically stable solutions of a perturbed nonlinear integral equation," (with  B. Masry and E. Mikael), Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 20 (2013), 83-93.

"Bounded solutions of almost linear Volterra equations," (with Y. N. Raffoul), Advances in Dynamical Systems and Applications, Vol. 7, No. 2 (2012), 195-205.

"Separate contraction and existence of periodic solutions in totally nonlinear delay differential equations," (with M. Adivar and Y. N. Raffoul), Hacettepe J. of Mathematics and Statistics, 41 (2012), 1-13.

"Three fixed point theorems: periodic solutions of a Volterra type integral equation with infinite heredity," Canad. Math. Bull., (Published electronically June 2011. doi:10.4153/CMB-2011-123-5), Vol. 56(1) (2013), 80-91.

"Periodic solutions of Volterra type integral equations with finite delay," Commun. Appl. Anal. 15 (2011). (1)

"Periodic solutions of neutral delay integral equations of advanced type," (with N. Sultana and J. Booth), EJDE, Vol 2010 (2010), No. 170, pp. 1 – 8.

"Bounded solutions and periodic solutions of almost linear Volterra equations," (with Y. N. Raffoul), CUBO - A Mathematical Journal, Special Issue: Qualitative Properties of Functional Equations, Vol. 11, No 3 (2009), 115-124.

"Qualitative properties of nonlinear Volterra integral equations," (with J. Neugebauer), Electronic J. of Qualitative Theory of Differential Equations, 12 (2008), 1-16. (1)

"Periodic solutions of neutral nonlinear systems of differential equations with functional delay," (with Y. N. Raffoul), J. Math. Anal. Appl., 331 (2007), 1175-1186. (12)

"Boundedness and stability in nonlinear delay difference equations employing fixed point theory," (with E. Yankson), Electronic J. of Qualitative Theory of Differential Equations, 26 (2005), 1-18. (1)

"Stability properties of linear Volterra integrodifferential equations with nonlinear perturbation," (with Y.  N. Raffoul), J. Integral Equations Appl., Vol 17, no 3 (2005).

"Uniform asymptotic stability in nonlinear Volterra discrete systems," (with P. W. Eloe & Y. N. Raffoul), Comput. Math. Appl., 45 (2003), 1033-1039. (8)

"Stability properties of linear Volterra integrodifferential equations with nonlinear perturbations," (with Y. N. Raffoul), Commun. Appl. Anal., 7 (2003), 405 -416. (6)

"Periodic solutions of Volterra type integral equations with finite delay," Commun. Appl. Anal., 15 (2001), 57-68.

"Monotone methods and fourth order Lidstone boundary value problems with impulse effects," (with P.W. Eloe), Commun. Appl. Anal., 5 (2001) 113-120. (5)

"Uniform asymptotic stability in linear volterra integrodifferential equations with application to delay systems," (with Bo Zhang and P. W. Eloe), Dynam. Systems Appl., 9 (2000),331-344. (6)

"Refractive system for annular Gaussian-to-Bessel beam transformation," (with M. Arif, M. Hossain, & A. A. S. Awwal), Appl. Opt., 37 (1998), 649-652. (10)

"Two-element refracting system for annular Gaussian-to-Bessel transformation," (with M. Arif, M. Hossain, & A. Awwal), Appl. Opt., 37 (1998), 4206-4209. (13)

"Almost periodic solutions of nonlinear integral equations," Nonlinear Anal., 30 (1997), 865-869.

"Stability properties and integrability of the resolvent of linear Volterra equations," (with P.W. Eloe), Tohoku Math. J., 47 (1995), 263-269. (3)

"On infinite delay integral equations having nonlinear perturbations," J. Integral Equations Appl., 5 (1993), 211-219. (1)

"2Modified signed-digit trinary arithmetic using optical symbolic substitution," (with A.A.S. Awwal & M.A. Karim), Appl. Opt., 31 (1992), 1687-1694. (31)

"Nonlinear integrodifferential equations and a priori bounds on periodic solutions," (with T.A. Burton & P.W. Eloe), Ann. Mat. Pura Appl., 161 (1992), 271-283. (3)

"Periodic solutions of linear integrodifferential equations," (with T.A. Burton & P.W. Eloe), Math. Nachr., 147 (1990), 175-184. (2)

"Periodic solutions of nonlinear integral equations," Ann. Mat. Pura Appl., 150 (1988),129-139. (1)