Select Publications
Journal articles
2017, 'A Discrete Approach to Continuous Second-Order Boundary Value Problems via Monotone Iterative Techniques', International Journal of Difference Equations, 12, pp. 145 - 160, http://campus.mst.edu/ijde/contents/v12n1p8.pdf
,2017, 'Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach', International Journal of Mathematical Education in Science and Technology, 48, pp. 913 - 918, http://dx.doi.org/10.1080/0020739X.2016.1272143
,2017, 'Existence and exact controllability of fractional evolution inclusions with damping', Mathematical Methods in the Applied Sciences, 40, pp. 4548 - 4559, http://dx.doi.org/10.1002/mma.4325
,2017, 'Critical perspectives of pedagogical approaches to reversing the order of integration in double integrals', International Journal of Mathematical Education in Science and Technology, 48, pp. 1285 - 1292, http://dx.doi.org/10.1080/0020739X.2017.1329559
,2017, 'Basic Existence and Uniqueness Results for Solutions to Systems of Nonlinear Fractional Differential Equations', Dynamics of Continuous, Discrete and Impulsive Systems - Series A: Mathematical Analysis, 24, pp. 181 - 193, http://online.watsci.org/contents2017/v24n3a.html
,2017, 'Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems', International Journal of Mathematical Education in Science and Technology, 48, pp. 794 - 801, http://dx.doi.org/10.1080/0020739X.2017.1285062
,2017, 'Constructive existence results for solutions to systems of boundary value problems via general Lyapunov methods', Differential Equations and Applications, 9, pp. 57 - 68, http://dx.doi.org/10.7153/dea-09-05
,2017, 'Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions', International Journal of Mathematical Education in Science and Technology, 48, pp. 1087 - 1095, http://dx.doi.org/10.1080/0020739X.2017.1298856
,2016, 'How useful are closed captions for learning mathematics via online video?', International Journal of Mathematical Education in Science and Technology, http://dx.doi.org/10.1080/0020739X.2016.1238518
,2016, 'Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions', Abstract and Applied Analysis, 2016, http://dx.doi.org/10.1155/2016/3910972
,2016, 'Basic existence and a priori bound results for solutions to systems of boundary value problems for fractional differential equations', Electronic Journal of Differential Equations, 2016, pp. 1 - 9, http://www.emis.ams.org/journals/EJDE/Volumes/2016/84/abstr.html
,2016, 'Existence of solutions to second-order boundary value problems without growth restrictions', Electronic Journal of Qualitative Theory of Differential Equations, 2016, pp. 1 - 14, http://dx.doi.org/10.14232/ejqtde.2016.1.92
,2015, 'When do fractional differential equations have solutions that are bounded by the Mittag - Leffler function ?', Fractional Calculus and Applied Analysis, 18, pp. 642 - 650, http://dx.doi.org/10.1515/fca-2015-0039
,2015, 'Analysis of the boundary value problem associated with the nonrelativistic Thomas-Fermi equation for heavy atoms in intense magnetic fields', Differential Equations and Applications, 7, pp. 27 - 41, http://dx.doi.org/10.7153/dea-07-03
,2015, 'Maximal solutions to fractional differential equations', Fractional Differential Calculus, 5, pp. 79 - 85
,2014, 'SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS THAT EXTEND', Journal of Classical Analysis, 5, pp. 129 - 136, http://dx.doi.org/10.7153/jca-05-11
,2014, 'Existence of solutions to derivative-dependent, nonlinear singular boundary value problems', Applied Mathematics Letters
,2012, 'A note on improved contraction methods for discrete boundary value problems', Journal of Difference Equations and Applications, 18, pp. 1773 - 1777, http://dx.doi.org/10.1080/10236198.2012.681781
,2012, 'On the application of sequential and fixed-point methods to fractional differential equations of arbitrary order', Journal of Integral Equations and Applications, 24, pp. 283 - 319, http://dx.doi.org/10.1216/JIE-2012-24-2-283
,2012, 'The existence of solutions to second-order singular boundary value problems', Nonlinear Analysis - Theory Methods and Applications, 75, pp. 4798 - 4806, http://dx.doi.org/10.1016/j.na.2012.03.029
,2011, 'Alternative solutions of inhomogeneous second-order linear dynamic equations on time scales', Journal of Difference Equations and Applications, 17, pp. 1487 - 1498
,2011, 'Asymptotic integration of second-order nonlinear difference equations', Glasgow Mathematical Journal, 53, pp. 223 - 243, http://dx.doi.org/10.1017/S0017089510000650
,2011, 'The method of upper and lower solutions for discrete BVP on infinite intervals', Journal of Difference Equations and Applications, 17, pp. 267 - 278, http://dx.doi.org/10.1080/10236190902911548
,2010, 'Exponential stability in functional dynamic equations on time scales', Communications in Mathematical Analysis, 9, pp. 93 - 108
,2010, 'On exact controllability of first-order impulsive differential equations', Advances in Difference Equations, 2010, pp. Article ID 136504, 9 pages, http://dx.doi.org/10.1155/2010/136504
,2009, 'Positive symmetric solutions of singular semipositone boundary value problems', Electronic Journal of Qualitative Theory of Differential Equations
,2009, 'Nondegeneracy of positive solutions to homogeneous second-order differential systems and its applications', ACTA Mathematica Scientia, 29, pp. 435 - 446
,2009, 'Successive approximations to solutions of dynamic equations on time scales', Communications on Applied Nonlinear Analysis, 16, pp. 61 - 87
,2008, 'Some results on periodic solutions for even order differential equations', Communications in Applied Analysis, 12, pp. 23 - 28
,2008, 'A multiplicity result for p-Lapacian boundary value problems via critical points theorem', Applied Mathematics and Computation, 205, pp. 231 - 237
,2008, 'Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales', Nonlinear Analysis - Theory Methods and Applications, 69, pp. 2303 - 2317, http://dx.doi.org/10.1016/j.na.2007.08.010
,2008, 'Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling', Nonlinear Analysis - Theory Methods and Applications, 68, pp. 3504 - 3524, http://dx.doi.org/10.1016/j.na.2007.03.043
,2008, 'Existence of periodic and non-periodic solutions to systems of boundary value problems for first-order differential inclusions with super-linear growth', Applied Mathematics and Computation, 204, pp. 441 - 449
,2008, 'Terminal value problems for first and second order nonlinear equations on time scales', Electronic Journal of Differential Equations, 2008, pp. 1 - 21
,2008, 'Volterra integral equations on time scales: Basic qualitative and quantatative results with applications to initial value problems on unbounded domains', International Journal of Difference Equations, 3, pp. 103 - 133
,2007, 'On the existence of multiple solutions to boundary value problems for second order ordinary differential equations', Dynamic Systems and Applications, 16, pp. 595 - 609
,2007, 'Constant-sign solutions of a system of Volterra integral equations', Computers and Mathematics With Applications, 54, pp. 58 - 75
,2007, 'Dynamic boundary value problems of the second-order: Bernstein-Nagumo conditions and solvability', Nonlinear Analysis - Theory Methods and Applications, 67, pp. 1374 - 1386, http://dx.doi.org/10.1016/j.na.2006.07.023
,2007, 'Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth', Electronic Journal of Differential Equations, 2007, pp. 1 - 14
,2007, 'Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions', Nonlinear Analysis - Theory Methods and Applications, 67, pp. 1236 - 1245, http://dx.doi.org/10.1016/j.na.2006.07.010
,2007, 'Methods for two resonant problems on time scales', International Journal of Difference Equations, 2, pp. 1 - 12
,2007, 'On systems of boundary value problems for differential inclusions', ACTA Mathematica Sinica - English Series, 23, pp. 549 - 556
,2007, 'On the solvability of periodic boundary value problems with impulse', Journal of Mathematical Analysis and Applications, 331, pp. 902 - 912
,2007, 'On the solvability of two-point, second-order boundary value problems', Applied Mathematics Letters, 20, pp. 824 - 828, http://dx.doi.org/10.1016/j.aml.2006.08.028
,2007, 'Oscillation and nonoscillation of forced second order dynamic equations', Pacific Journal of Mathematics, 230, pp. 59 - 71
,2007, 'Solvability of discrete Neumann bo undary value problems', Journal of Mathematical Analysis and Applications, 331, pp. 736 - 741
,2007, 'Third-order nonlocal problems with sign-changing nonlinearity on time scales', Electronic Journal of Differential Equations, 2007, pp. 1 - 12
,2007, 'Two classical periodic problems on time scales', Electronic Journal of Differential Equations, 2007, pp. 1 - 12
,2006, 'Existence and uniqueness to nonlinear dynamic boundary value problems', CUBO A Mathematical Journal, 8, pp. 11 - 24
,2006, 'Existence of non-spurious solutions to discrete boundary value problems', Electronic Journal of Differential Equations, 3, pp. 1 - 9
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