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Mark A. McKibben

Research

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Mark A. McKibben

Office: UNA 113
Phone: (610) 436-2148
Fax: (610) 738-0578
E-mail: mMcKibben@wcupa.edu

Research Interests & Journal Articles

Research Interests

My current research interests lie in the area of stochastic evolution equations , stochastic partial differential equations, and control theory.

Published Journal Articles

  1. McKibben, M.A. & Webster, M., Abstract functional second-order stochastic evolution equations with applications, to appear in Afrika Matematika.
  2. Lakhel, E. & McKibben, M.A., Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion, Afrika Matematika, volume 28, number 1 – 2, 207 – 220, March 2017.
  3. McKibben, M.A. & N.I. Mahmudov, On the approximate controllability of fractional evolution equations with generalized Riemann-Liouville fractional derivative, in Special Issue “Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems,” Journal of Function Spaces, vol. 2015, Article ID 263823, 9 pages, 2015. doi:10.1155/2015/263823, May 2015.
  4. McKibben, M.A. & Webster, M, Abstract Stochastic Integrodifferential Delay Equations Driven by Fractional Brownian Motion, Far East Journal of Mathematical Sciences, volume 96, number 6, 757 – 800, March 2015.
  5. Mahmudov, N.I., McKibben, M.A., Rathinasamy, S., and Ren, Y., Control, Stability, and Qualitative Theory of Dynamical Systems - II: Editorial, Abstract and Applied Analysis, Special Issue on CQST, 1-2, February 2015.
  6. McKibben, M.A. & Webster, M., Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion, Abstract and Applied Analysis, vol. 2014, Article ID 516853, 14 pages, doi:10.1155/2014/516853, 2014.
  7. McKibben, M.A., Measure-Dependent Stochastic Nonlinear Beam Equations Driven by Fractional Brownian Motion, International Journal of Stochastic Analysis, vol. 2013, Article ID 868301, 16 pages, 2013. doi:10.1155/2013/868301.
  8. Mahmudov, N.I., McKibben, M.A., Rathinasamy, S., and Ren, Y., Control, Stability, and Qualitative Theory of Dynamical Systems: Editorial, Abstract and Applied Analysis, Special Issue on CQST, 1-2, Nov 2013.
  9. Henriquez, H., Hernandez, E., and McKibben, M., Existence results for abstract impulsive second-order neutral functional differential equations, Nonlinear Analysis and Applications Series A: Theory, Methods, and Applications, vol. 70, no. 1, 2736-2751, (April 2009).
  10. Henriquez, H., Hernandez, E. and McKibben, M., Existence of solutions of second-order partial neutral functional differential equations with unbounded delay, Integral Equations and Operator Theory, vol. 6. no. 2, 191-217, (April 2009)
  11. Henriquez, H., Hernandez, E., and McKibben, M., Existence results for partial neutral functional differential equations with state-dependent delay, Mathematical and Computer Modeling, vol. 49, 5-6, 1260-1267, (March 2009).
  12. Mahmudov, N. and McKibben, M., On a class of backward McKean-Vlasov stochastic equations in Hilbert space: Existence and convergence properties, Dynamic Systems and Appl., vol. 16, (Dec. 2007), 643 – 664.
  13. Hernandez, E., Keck, D. and McKibben, M., On a class of measure-dependent stochastic evolution equations driven by fBm, Journal of Applied Mathematics and Stochastic Analysis, vol. 2007 (Oct. 2007), Article ID 69747, 26 pages.
  14. Mahmudov, N. and McKibben, M., On backward stochastic evolution equations in Hilbert space and optimal control, Nonlinear Analysis Series A: Theory, Methods, and Applications, vol. 67, no. 4, (August 2007), 1262 - 1274.
  15. Hernandez, E. and McKibben, M., On state-dependent partial neutral functional-differential equations, Applied Mathematics and Computation, vol. 186, no. 1, (March 2007), 294 - 301.
  16. Keck, D. and McKibben, M., Abstract semilinear Itó-Volterra integro-differential stochastic evolution equations, vol. 2006 (Nov. 2006), Journal of Applied Mathematics and Stochastic Analysis, Article ID 45253, 22 pages.
  17. Mahmudov, N. and McKibben, M., Approximate controllability for second-order neutral stochastic evolution equations, Continuous, Discrete, and Impulsive Dynamic Systems: Series B – Applications and Algorithms, vol. 13, no. 5, (Oct. 2006), 619 - 634.
  18. Mahmudov, N. and McKibben, M., Controllability results for a class of abstract first-order McKean-Vlasov stochastic evolution equations, Dynamic Systems and Appl., vol. 15, (Oct. 2006), 357 - 374.
  19. Mahmudov, N. and McKibben, M., Abstract second-order damped McKean-Vlasov stochastic evolution equations, Stochastic Analysis and Applications, vol. 24, no. 2, (April 2006), 303 – 328.
  20. Hernandez, E. and McKibben, M., Some comments on: Existence of solutions of abstract nonlinear second-order neutral functional integro-differential equations, Computers and Mathematics with Applications, vol. 50, no. 8-9, (Nov. 2005), 655 - 669.
  21. Keck, D. and McKibben, M., Abstract stochastic integrodifferential delay equations Journal of Applied Mathematics and Stochastic Analysis, vol. 2005 no. 3, (Sept. 2005), 275 - 305.
  22. McKibben, M., Second-order neutral stochastic evolution equations with heredity, Journal of Applied Mathematics and Stochastic Analysis, vol. 17, no. 2 (Sept. 2004), 177 - 192.
  23. McKibben, M., Second-order damped functional stochastic evolution equations in Hilbert space, Dynamic Systems and Applications, vol. 12, no. 3 – 4 (Dec. 2003), 467 – 488.
  24. Keck, D. and McKibben, M., Functional integro-differential stochastic evolution equations in Hilbert space, Journal of Applied Mathematics and Stochastic Analysis, vol. 16, (Nov. 2003), 1 – 21.
  25. Keck, D. and McKibben, M., On a McKean-Vlasov stochastic integro-differential evolution equation of Sobolev type, Stochastic Analysis and Applications, vol. 21, no. 5, (Oct. 2003), 1115 – 1139.
  26. McKibben, M., Approximate controllability results for a class of abstract second-order functional evolution equations, Journal of Optimization Theory and Applications, vol. 117, no. 2, (May 2003), 397 – 414.
  27. McKibben, M., A note on the approximate controllability of a class of abstract semi-linear evolution equations, Far East Journal of Applied Mathematics, vol. 5, issue 2, (May 2002), 113 - 133.
  28. Aizicovici, S., McKibben, M., and Reich, S., Anti-periodic solutions to non-monotone evolution equations with discontinuous nonlinearities, Nonlinear Analysis, vol. 43, no. 2,(Jan. 2001), 233 - 251.
  29. McKibben, M., Controllability of abstract evolution systems with nonlocal initial data Far East Journal of Applied Mathematics, vol. 4, no. 3, (Nov. 2000), 317 – 343.
  30. McKibben, M., On some nonlinear nonlocal autonomous Cauchy problems in Banach spaces, Far East Journal of Mathematical Sciences, vol. 2., no. 4, (July 2000), 555 - 575.
  31. Aizicovici, S., Grasselli, M., and McKibben, M., A hyperbolic integro-differential system related to phase field models, Advanced Mathematical Sciences and Applications, vol. 10, no. 2 (2000), 601 – 625. (Also is Technical Report #367P, Politecnico di Milano, 2000.)
  32. Aizicovici, S. and McKibben, M., Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Analysis, vol. 39, issue 5, (Feb. 2000), 649 - 668.
  33. Aizicovici, S. and McKibben, M., Semi-linear Volterra integro-differential equations with nonlocal initial conditions, Abstract and Applied Analysis, vol. 4, issue 2, (1999), 127 – 139.
  34. McKibben, M., Nonlocal Cauchy problems for abstract functional differential equations, presented in International Workshop on Differential Equations & Optimal Control, Ohio University, 1999.

Chapters in Books

  1. E. Lakhel and M. A. McKibben, “Controllability of Impulsive Neutral Stochastic Functional Integro-Differential Equations Driven by Fractional Brownian Motion,”  Chapter 8 in: Brownian Motion: Elements, Dynamics, and Applications, Editors: M.A. McKibben and M. Webster, Nova Science Publishers, forthcoming 2016.
  2. M. A. McKibben and M. Webster, “Abstract Second-Order Stochastic Evolution Equations in a Hilbert Space Driven by Fractional Brownian Motion,” Chapter 15 in : Brownian Motion: Elements, Dynamics, and Applications, Editors: M.A. McKibben and M. Webster, Nova Science Publishers, forthcoming 2016.
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