Dr. Leigh C. Becker
Publications, Presentations and Teaching Awards
Teaching Awards
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May 2012 ─ The Dr. Marguerite Cooper Distinguished Professor Award for Excellence In Teaching.
May 2002 ─ The Dr. Marguerite Cooper Distinguished Professor Award for Excellence In Teaching.
Research Papers
Leigh C. Becker
Solutions of Fractional Relaxation Equations via Resolvents and a Variation of Parameters Formula.
(work in progress).
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Leigh C. Becker and Ioannis K. Purnaras
Fractional Relaxation Equations and a Cauchy Formula for Repeated Integration of the Resolvent.
Advances in the Theory of Nonlinear Analysis and its Applications, Vol. 2 (2018) No. 1, 11-32.
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Leigh C. Becker
Properties of the resolvent of a linear Abel integral equation: implications for a complementary fractional equation.
Electron. J. Qual. Theory Differ. Equ., No. 64, 2016, pp. 1-38.
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L. C. Becker, T. A. Burton, and I. K. Purnaras
Integral and fractional equations, positive solutions, and Schaefer`s fixed point theorem,
Opuscula Mathematica, 36, No. 4 (2016), pp. 431-458.
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L. C. Becker, T. A. Burton, and I. K. Purnaras
Existence of Solutions of Nonlinear Fractional Differential Equations of Riemann-Liouville Type,
Journal of Fractional Calculus and Applications, Vol. 7(2), July 2016, pp. 20-39.
L. C. Becker, T. A. Burton, and I. K. Purnaras
Fractional differential equations, transformations, and fixed points,
Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis,
Vol. 22, No. 5 (2015), pp. 333-361.
L. C. Becker, T. A. Burton, and I. K. Purnaras
An Inversion of a Fractional Differential Equation and Fixed Points,
Nonlinear Dynamics and Systems Theory, Vol. 15, No. 3, 2015, pp. 242-271.
L. C. Becker, T. A. Burton, and I. K. Purnaras
Complementary equations: a fractional differential equation and a Volterra integral equation,
Electron. J. Qual. Theory Differ. Equ., No. 12, 2015, pp. 1-24.
Leigh C. Becker
Resolvents and solutions of singular Volterra integral equations with separable kernels
Applied Mathematics and Computation, 219, Issue 24 (15 August 2013), pp. 11265-11277.
Leigh C. Becker
Resolvents for weakly singular kernels and fractional differential equations
Nonlinear Analysis: Theory, Methods & Applications, Vol. 75, Issue 13 (September 2012), pp. 4839-4861.
Leigh C. Becker, T. A. Burton, I. K. Purnaras
Singular integral equations, Liapunov functionals, and resolvents
Nonlinear Analysis: Theory, Methods & Applications, 75, Issue 7 (May 2012), pp. 3277-33291.
Digital Object Identifier Information: 10.1016/j.na.2011.10.050
Leigh C. Becker
Resolvents and solutions of weakly singular linear Volterra integral equations
Nonlinear Analysis: Theory, Methods & Applications, 74, Issue 5 (March 2011), pp. 1892-1912.
Digital Object Identifier Information: 10.1016/j.na.2010.10.060
Leigh C. Becker
Uniformly Continuous L1 Solutions of Volterra Equations and Global Asymptotic Stability
CUBO, A Mathematical Journal, Vol 11, No. 3 (August 2009), pp. 1-24.
This paper appears in the special issue: Qualitative Properties of Functional Equations.
The series of papers in this issue begins with a preface and overview by T.A. Burton (guest editor).
Leigh C. Becker
Function bounds for solutions of Volterra equations and exponential asymptotic stability
Nonlinear Analysis: Theory, Methods & Applications 67, Issue 2 (July 2007), pp. 382-397.
Digital Object Identifier Information: 10.1016/j.na.2006.05.016
Leigh C. Becker
Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint
Electronic Journal of Qualitative Theory of Differential Equations, No. 14 (2006), pp. 1-22.
Note: A version of the paper can also be found on pp. 36 - 54 in the monograph:
Liapunov Theory for Integral Equations with Singular Kernels and Fractional Differential Equations
by T. A. Burton, amazon.com (2012). To view this version on the web, click on the above link and search for Becker; then select page 36.
Leigh C. Becker and T. A. Burton
Stability, fixed points and inverses of delays
Proceedings of the Royal Society of Edinburgh, 136A, No. 2 (May 2006), pp. 245-275.
Abstract (PDF format) Abstract (DVI format) Abstract (IngentaConnect [www.ingentaconnect.com])
Leigh C. Becker and T. A. Burton
Jensen's Inequality and Liapunov's Direct Method
CUBO, A Mathematical Journal, Vol 6, No. 3 (October 2004), pp. 67-90.
Abstract (PDF format) Abstract (DVI format) Abstract (PostScript format) Abstract (MS Word)
Download preprint (PDF format)
Photos of authors:
Leigh Becker & T. A. Burton at the AMS Meeting in Portland, Oregon June 20-22, 2002
Leigh Becker at the Oregon coast June 23, 2002
L. C. Becker, T. A. Burton, and S. Zhang
Functional differential equations and Jensen's inequality
Journal of Mathematical Analysis and Applications, 138, Issue 1 (1989), Academic Press, Orlando, pp. 137-156.
L. C. Becker and T. A. Burton
Asymptotic stability criteria for delay-differential equations
Proceedings of the Royal Society of Edinburgh 110A (1988), pp. 31-44.
L. C. Becker, T. A. Burton, and T. Krisztin
Floquet Theory for a Volterra equation
Journal of the London Mathematical Society (2) 37 (1988), pp. 141-147.
L. C. Becker, T. A. Burton, and S. Zhang
Functional differential equations and Jensen's Inequality
Dynamics of Infinite Dimensional Systems (Hale, J. K. and Chow, S. N., eds.)
NATO ASI Series, Vol. F37 (1987), Springer-Verlag, New York, pp. 31-38.
Other Publications
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Leigh C. Becker
Review of the monograph:
Liapunov theory for integral equations with singular kernels and fractional differential equations
by Theodore Allen Burton in Mathematical Reviews (MR3088486), American Mathematical Society (2014).
(Amazon.com link to monograph)
Leigh C. Becker
Constant Delay Differential Equations and the Method of Steps
Maple Application Center (June 8, 2009).
(To view the HTML version or to download the Maple worksheet, click on the above hyperlink.)
Leigh C. Becker
Scalar Volterra Integro-Differential Equations
Maple Application Center (August 2007).
(To view the HTML version or to download the Maple worksheet, click on the above hyperlink.)
Leigh C. Becker and Micah Wheeler
Numerical and Graphical Solutions of Volterra Integral Equations of the Second Kind
Maple Application Center (June 2005).
(To view the HTML version or to download the Maple worksheet, click on the above hyperlink.)
Leigh C. Becker
Setting the Stage with APR Problems
Mathematics and Computer Education (1984, Fall), 18(3), pp. 189 - 195.
Ph.D. Dissertation
Leigh C. Becker
Stability Considerations for Volterra Integro-differential Equations
Ph.D. dissertation, Southern Illinois University at Carbondale, Advisor: T. A. Burton, Dissertation Research Award 1979.
Download dissertation (pdf format)
Note: Revised and more concise versions of the part of the dissertation dealing with the principal matrix solution (aka the resolvent)
can also be found in
(1) the paper ''Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint'',
Electronic Journal of Qualitative Theory of Differential Equations, No. 14 (2006), pp. 1 - 22
and
(2) the monograph Liapunov Theory for Integral Equations with Singular Kernels and Fractional Differential Equations by T. A. Burton, amazon.com (2012).
(To view this version on the web, click on the above link and search for Becker; then select page 36.)
Acknowledgements of solutions of problems
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Problem 82-19: A binomial coefficient summation, SIAM Review 25 (1983), p. 576.
Problem 184: TYCMJ (now the College Mathematics Journal) 13, No. 3 (1982), p. 211.
Problem 194: TYCMJ (now the College Mathematics Journal) 13, No. 5 (1982), p. 341.
Unpublished Textbook with ancillaries
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Leigh C. Becker
Ordinary Differential Equations: Concepts, Methods, and Models
XanEdu Press, 2015 - 2016 edition, 518 pages (work in progress)
Leigh C. Becker
Complete Solutions of Selected Problems for Ordinary Differential Equations: Concepts, Methods, and Models
Web site: http:///facstaff.cbu.edu/~lbecker/231Ans.htm
Leigh C. Becker
Maple worksheets for Ordinary Differential Equations: Concepts, Methods, and Models
Web site: http://facstaff.cbu.edu/~lbecker/231maple.ht
Miscellanea
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L. C. Becker
ODE Experiments Using Maple, CBU Press, 1998.
L. C. Becker
The function y = (1 + 1/x)x and the number e, (Lab 4 in Laboratory Manual for Calculus II), Christian Brothers University (1991), 29-39.
Reviewed research papers & monographs for the following:
Applied Mathematics and Computation
Applied Mathematics Letters
Differential Equations & Applications
Electronic Journal of Differential Equations
Electronic Journal of Qualitative Theory of Differential Equations
Filomat
International Journal of Dynamical Systems and Differential Equations
Journal of Integral Equations and Applications
Journal of Mathematical Analysis and Applications
Journal of Taibah University for Science
Mathematical Reviews
Nonlinear Analysis
Positivity
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Presentations
November 15, 2016 ─ Rhodes College, Introduction to fractional derivatives.
October 17, 2015 ─ American Mathematical Society Southeastern Sectional Meeting hosted by the University of Memphis.
Special session speaker on analysis of differential and integral equations: Existence of solutions of nonlinear fractional differential
equations of Riemann-Liouville type.
October 11, 2014 ─ The 34th Southeastern Atlantic Regional Conference on Differential Equations hosted by the University of Memphis.
Title of talk: A resolvent and fractional differential equation.
November 7, 2009 ─ Differential Equations Weekend Conference hosted by the University of Memphis.
Title of talk: Uniformly continuous and asymptotically stable solutions of Volterra integro-differential equations.
July 4, 2008 ─ WCNA 2008 in Orlando, Florida (Fifth World Congress of Nonlinear Analysts, July 2 - July 9). Presented a 45-minute
invited lecture entitled Uniformly continuous L1 solutions of Volterra equations and global asymptotic stability in the session
''Qualitative Properties and Application of Functional Equations'' and chaired part of this session.
Photos:
Speakers at the ''Qualitative Properties & Application of Functional Equations'' session (July 4 & 5, 2008):
Muhammad Islam, Min He, Alphonso Casal, Colleen Kirk, T. A. Burton, Tetsuo Furumochi, Leigh C. Becker, Bo Zhang, Youssef Raffoul, Liancheng Wang, & Henri Schurz (not shown).
Lynne Marie Becker at the Hyatt Grand Cypress Resort Pool in Orlando (July 7, 2008).
March 16, 2007 ─ Asymptotic Stability for Scalar Linear Volterra Integro-Differential Equations, Mathematical Association of America Southeastern Section 86th Annual Meeting, Georgia Southern University, Statesboro, GA.
January 5-8, 2005 ─ Joint Mathematics Meetings in Atlanta, Georgia. Co-chaired the American Mathematical Society Session on Ordinary Differential Equations (Jan. 7). Presented a paper (coauthor T.A. Burton, Northwest Research Institute) entitled Fixed Points and Stability of a Volterra Equation with Variable Delay.
July 1, 2004 ─ WCNA 2004 in Orlando, Florida (Fourth World Congress of Nonlinear Analysts, June 30 - July 7). Presented a 45-minute invited lecture
entitled Stability, Fixed Points, and Inverses of Delays in the session ''Application of Fixed Point Theory to Functional Equations'' and chaired part of this session.
March 26, 2004 ─ Fixed Points and Stability of an Equation with Variable Delay (with T. A. Burton), Mathematical Association of America Southeastern Section meeting,
Austin Peay State University, Clarksville, TN.
June 21, 2002 ─ Jensen's Inequality and Liapunov's Direct Method, ''Special Session on ''Qualitative Properties and Applications of Functional Equations'', American Mathematical Society Meeting in Portland, Oregon.
November 6, 2001 ─ Mathematical Scientists & What They Do, Mu Alpha Theta Induction Ceremony 2001 at Ridgeway High School.
October 21, 2000 ─ At the request of Institutional Advancement, talked at Sacred Heart Catholic Church in Memphis about CBU.
September 25, 1997 ─ Maple in CBU Mathematics Courses, CBU President's Circle.
August 22, 1996 ─ presented a demonstration of a Maple lesson entitled Integral Curves and Contours of Exact Equations, CBU President's Workshop.
February 9, 1996 ─ talk to the CBU student chapter of the MAA entitled She loves me, she loves me not (linear system of ordinary differential equations).
August 30, 1990 ─ Simulating and Stimulating with Baseball Cards, Mathematics & Computer In-Service, Ridgeway High School, Memphis.
November 10-11, 1989 ─ Asymptotic Stability Criteria for Delay-Differential Equations, 18th Midwest Differential Equations Conference, Southern Illinois University at Carbondale.
August 1988 ─ conducted two days of a four-day workshop for Memphis high school mathematics teachers on elementary differential equations in the BC calculus curriculum. Participants were shown how to use the HP-28S calculator when solving and graphing ordinary differential equations.
December 2, 1987 ─ Floquet Theory for Volterra Equations I, Differential Equations Seminar, Memphis State University.
November 25, 1987 ─ Floquet Theory for Volterra Equations I, Differential Equations Seminar, Memphis State University.
October 23-24, 1987 ─ co-author of Floquet Theory for Volterra Equations, Midwest-Southeast Differential Equations Conference, Vanderbilt University, Nashville, TN.
1983 ─ consulting work on a mathematical model of a shutter for a certain type of camera for DeZign Corporation.
May 13, 1982 ─ A Variation of Parameters Formula for Volterra Integral Equations, Mathematical Sciences Colloquium, Memphis State University.
April, 1982 ─ Setting the Stage with APR Problems, regional Mathematical Association of America meeting at Emory University in Atlanta, Georgia.
January 25, 1979 ─ Some Results for Volterra Integrodifferential Equations, American Mathematical Society Session on Ordinary Differential Equations, Biloxi, Mississippi.