# Publications

## Applications of Fractional Calculus (Publications in the last dozen years)

1. B. N. Narahari Achar, John W. Hanneken, Thomas Enck, Ted Clarke, “Dynamics of the Fractional Oscillator”, Physica A 297 (2001) 361-367. http://dx.doi.org/10.1016/S0378-4371(01)00200-X

2. B. N. Narahari Achar, John W. Hanneken, and Ted Clarke, “Response Characteristics of a Fractional Oscillator”, Physica A 309 (2002) 275-288. http://dx.doi.org/10.1016/S0378-4371(02)00609-X

3. B.N. Narahari Achar, John W. Hanneken, “Surprising Non-Scaling Behavior in Fractional Diffusion”, Physica A 322 (2003) 195-200 and 326 (2003) 609-610. http://dx.doi.org/10.1016/S0378-4371(02)01911-8 and http://dx.doi.org/10.1016/S0378-4371(03)00390-X

4. B. N. Narahari Achar, Carl F Lorenzo and Tom Hartley, “Initialization and the Caputo Fractional Derivative”, (2003) NASA/TM-2003-212482

5. John W. Hanneken, B. N. Narahari Achar, David M. Vaught, Kristine L. Harrington, “A Random Walk Simulation of Fractional Diffusion”, Journal of Molecular Liquids 114 (2004) 153-157 http://dx.doi.org/10.1016/j.molliq.2004.02.013

6. B.N. Narahari Achar, John W. Hanneken, “Fractional Radial Diffusion in a Cylinder”, Journal of Molecular Liquids 114 (2004) 147-151 http://dx.doi.org/10.1016/j.molliq.2004.02.012

7. Ted Clarke, B. N. Narahari Achar, John W. Hanneken, “Mittag-Leffler Functions and Transmission Lines”, Journal of Molecular Liquids 114 (2004) 159-163 http://dx.doi.org/10.1016/j.molliq.2004.02.014

8. B. N. Narahari Achar, John W. Hanneken, T. Clarke, “Damping characteristics of a fractional oscillator”, Physica A 339 (2004) 311-319 http://dx.doi.org/10.1016/j.physa.2004.03.030

9. B.N. Narahari Achar and John W. Hanneken, “Damping in a Fractional Relaxor-Oscillator Driven by a Harmonic Force”, Proceedings of IDETC/CIE 2005: 2005 ASME International Design Engineering Technical Conferences & Computer and Information in Engineering Conference held September 24-28, 2005 in Long Beach, California. DETC2005-84345 pp.1-7 ISBN: 0-7918-3766-1

10. John W. Hanneken, David M. Vaught and B. N. Narahari Achar, “The Number of Real Zeros of the Single Parameter Mittag-Leffler Function for Parameter Values Between 1 and 2”, Proceedings of IDETC/CIE 2005: 2005 ASME International Design Engineering Technical Conferences & Computer and Information in Engineering Conference held September 24-28, 2005 in Long Beach, California. DETC2005-84172 pp.1-5 ISBN: 0-7918-3766-1

11. B. N. Narahari Achar, Carl F Lorenzo, “ Initailization Issues of the Caputo Fractional Derivative”, Proceedings of IDETC/CIE 2005: 2005 ASME International Design Engineering Technical Conferences & Computer and Information in Engineering Conference held September 24-28, 2005 in Long Beach, California. DETC2005-84348 pp.1-5 ISBN: 0-7918-3766-1

12. John W. Hanneken, David M. Vaught and B. N. Narahari Achar, “Enumeration of the Real Zeros of the Mittag-Leffler Function Ea(z), 1 < a < 2 “, in Sabatier, J., Agrawal, O. P.,Tenreiro Machado, J. A. (Eds), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007 pp. 15-26. ISBN: 978-1-4020-6041-0

13. B. N. Narahari Achar and John W. Hanneken, “Dynamic Response of the Fractional Relaxor-Oscillator to a Harmonic Driving Force”, in Sabatier, J., Agrawal, O. P.,Tenreiro Machado, J. A. (Eds), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007 pp. 243-256. ISBN: 978-1-4020-6041-0

14. B. N. Narahari Achar, Tanya Prozny, John W. Hanneken, “Linear Chain of Coupled Fractional Oscillators; Response Dynamics and its Continuum Limit”, Proceedings of the ASME 2007 International Design Engineering Technical Conference & Computers and Information in Engineering Conference held September 4-7, 2007 in Las Vegas, Nevada DETC2007-35403 pp. 1-7

15. B. N. Narahari Achar, Carl F Lorenzo and Tom Hartley, “The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equations”, in Sabatier, J., Agrawal, O. P.,Tenreiro Machado, J. A. (Eds), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007 pp. 27-42. ISBN: 978-1-4020-6041-0

16 . B. N. Narahari Achar and John W. Hanneken, “Lattice Dynamical Foundation for the Fractional Calculus Approach to Viscoelasticity”, Proceedings of the Third IFAC Workshop on Factional Differentiation and Its Applications, Cankaya University, Ankara, Turkey, November 5-7, 2008.

17. John W. Hanneken, B. N. Narahari Achar, Raymond Puzio, and David Vaught, “Properties of the Mittag-Leffler function for negative alpha”, Proceedings of the Third IFAC Workshop on Factional Differentiation and Its Applications, Cankaya University, Ankara, Turkey, November 5-7, 2008.

18. John W. Hanneken, B. N. Narahari Achar, David M. Vaught, James M. Andrews and Avery T. Carr, “Sums of the zeros of the single parameter Mittag-Leffler function with the parameter equal to one-half”, Proceedings of the ASME 2009 Design Engineering Technical Conferences & Computers and Information in Engineering Conference, SanDiego, CA, August 30 – September 2, 2009, DETC2009-86220 pp. 1-7. ISBN 978-0-7918-3856-3

19. B. N. Narahari Achar and John W. Hanneken, “Response dynamics in the continuum limit of the lattice dynamical theory of viscoelasticity (fractional calculus approach)”, ”, Proceedings of the ASME 2009 Design Engineering Technical Conferences & Computers and Information in Engineering Conference, SanDiego, CA, August 30 – September 2, 2009, DETC2009-86218 pp. 1-7. ISBN 978-0-7918-3856-3

20. B. N. Narahari Achar and John W. Hanneken, “Microscopic formation of fractional calculus theory of viscoelasticity based on lattice dynamics”, Physica Scripta T136 (2009) 014011 (7pp)

21. John W. Hanneken, B. N. Narahari Achar, Raymond Puzio, and David Vaught, “Properties of the Mittag-Leffler function for negative alpha”, Physica Scripta T136 (2009) 014037 (5pp)

22. B. N. Narahari Achar and John W. Hanneken, “Fractional order dynamics under gravity: Falling Body and Kepler problems”, Proceedings of the International Workshop on Fractional Differentiation and its Applications (FDA’10) held at University of Extremadura, Badajoz, Spain, October 18-20, 2010.

23. B. N. Narahari Achar, John W. Hanneken, Nicholas Becker and Matthew Morgan, “Intrinsic dissipation in fractional order dynamics:, Proceedings of the International Workshop on Fractional Differentiation and its Applications (FDA’10) held at University of Extremadura, Badajoz, Spain, October 18-20, 2010.

24. John W. Hanneken, B. N. Narahari Achar, David M. Vaught, Stephan T. Spencer and Trenton R. Ensley , “An alpha-beta phase diagram representation of the zeros and properties of the Mittag-Leffler function”, Proceedings of the International Workshop on Fractional Differentiation and its Applications (FDA’10) held at University of Extremadura, Badajoz, Spain, October 18-20, 2010.

25. John W. Hanneken, James M. Andrews, David M. Vaught, B. N. Narahari Achar and Raymon Puzio, “Mittag-Leffler functions: Their infinite product representations and the sums of their zeros”, Proceedings of the International Workshop on Fractional Differentiation and its Applications (FDA’10) held at University of Extremadura, Badajoz, Spain, October 18-20, 2010.

26. B. N. Narahari Achar and John W. Hanneken, “Microscopic Formulation of Fractional Theory of Viscoelasticity”, in Viscoelasticity – From Theory to Biological Applications, by Juan de Vicente (Ed), Intech Publishing, NY, 2012 ISBN: 978-953-51-0841-2 http://dx.doi.org/10.5772/51493

27. B. N. Narahari Achar, Bradley T. Yale, and John W. Hanneken, “Time Fractional Schrodinger Equation Revisited”, Advances in Mathematical Physics 2013 (2013), 290216 (11 pages) http://dx.doi.org/10.1155/2013/290216

28. John W. Hanneken, B. N. Narahari Achar and David M. Vaught, “An Alpha-Beta Phase Diagram Representation of the Zeros and Properties of the Mittag-Leffler Function”, Advances in Mathematical Physics 2013 (2013), 421685 (13 pages) http://dx.doi.org/10.1155/2013/421685

29. John W. Hanneken and B. N. Narahari Achar, "Finite Series Representation of the Inverse Mittag-Leffler Function", Mathematical Problems in Engineering 2014 (2014), 252393 (18 pages) http://dx.doi.org/10.1155/2014/252393

## Archaeoastronomy (Publications in the last fifteen or so years)

1. B. N. Narahari Achar “A Mesopotamian Origin for Vedaanga Jyotisha: Is It Justified?” Jour. Ind. Phil. and Rel. (1997) 2, 29.

2. B. N. Narahari Achar, “A Note on the Five-year Yuga of VedAGga jyotiSa”, EJVS, 3-4, (1997).

3. B. N. Narahari Achar, “ Enigma of the Five-year Yuga of Vedanga Jyotisa,” Ind. Jour. Hist. Sci. 33, (1998), 101-109.

4. B. N. Narahari Achar, “ On the meaning of AV XIX.53.3: Measurement of Time?” EJVS, 4-2, (1998).

5. B. N. Narahari Achar, “ On the Vedic Origin of the Ancient Mathematical Astronomy of India”, Jour. Stu. Anc. India 1, 95 (1998)

6. B. N. Narahari Achar, “On an Astronomical Concept in Vishnupurana,” Ind. Jour. Hist. Sci. 34, 109-115, (1999)

7. B. N. Narahari Achar, “ On Exploring the Vedic Sky with Modern Computer software”, EJVS, 5,-2,(1999).

8. B. N. Narahari Achar, “Concept of the Five-Year Yuga system of Vedanga Jyotisa”, in New Perspectives on Vedic and Ancient Indian Civilization, Bhu Bev Sharma (ed), World Association for Vedic Studies, New York, (2000), pp 148-156.

9. B. N> Narahari Achar, “ Measurement of Time Using a Water Clock : An interpretation of the Third Mantra of the Kala sukta of Atharvaveda (XIX.53.3)”, in New Perspectives on Vedic and Ancient Indian Civilization, Bhu Bev Sharma (ed), World Association for Vedic Studies, New York, (2000), pp 157-165

10. M. Rajagopalan and B. N. Narahari Achar, “ Aryabhata's Kuttaka Method for Solving Linear Indeterminate Equations with Integral Coefficients”, in New Perspectives on Vedic and Ancient Indian Civilization, Bhu Bev Sharma (ed), World Association for Vedic Studies, New York, (2000), pp 1171-178.

11. B. N. Narahari Achar, “ On the Astronomical Basis of the date of Satapatha Brahmana: A Re-examination of Dikshit's Theory,” Ind. Jour. Hist. Sci. 35, 1-10 (2000).

12. B. N. Narahari Achar, “ A Case for Revising the Date of Vedanga Jyotisa,” Ind. Jour. Hist. Sci. 35, 173-183 (2000).

13. B. N. Narahari Achar, “ On the Caitradi Scheme,” Ind. Jour. Hist. Sci.35, 295-310 (2000).

14. B. N. Narahari Achar, “Comments on 'The Pleiades and the Bears viewed from inside the Vedic Texts',” EJVS 6, 2 (2000).

15. B. N. Narahari Achar,” Searching for Nakshatras in Rgveda,” EJVS,6, 2 (2000)

16. B. N. Narahari Achar, “Aryabhata and the Table of Rsines”, Indian Journal of History of Science, 37, (2002) 95-99.

17. B. N. Narahari Achar, “In search of Nakshatras in RgVeda”, in Contemporary Views of Indian Civilization, Bhu Dev Sharma (Ed) World Association for Vedic Studies, New York (2003) pp 361-370

18. B. N. Narahari Achar, “In Search of the Nakshatra's in Rg Veda,” Annals of the BORI Vol LXXXIII for the Year 2002, (2003) pp. 183-193

19. B. N. Narahari Achar, “On the Identification of Vedic Nakshatras,” in Contemporary Views of Indian Civilization, Bhu Dev Sharma (Ed) World Association for Vedic Studies, New York (2003) pp 371-387

20. B. N. Narahari Achar, “Date of the Mahabharata War based on Simulations using Planetarium Softwar”, Journal of the Mythic Society, Vol. XCIV (No. 1-2, Jan-Jun 2003) (2004) 65-115.

21. B. N. Narahari Achar, “ 3067 BCE as the year of the Mahabharata War,” Journal of the Mythic Society, Vol XCIV, (2004) 144-149.

22. B. N. Narahari Achar, “On Astronomical References in Vyasa-Dhrtarashtra samvada in the Bhishmaparvan of Mahabharata,” Annals of B.O.R.I., LXXXIV for the Year 2003, 14-22 (2004)

23. B. N. Narahari Achar, “On the Meaning of RV X.136: Comets?”

Annals of B. O. R. I. LXXXVII, (2006) pp 55-58

24. B. N. Narahari Achar, “Astronomy of the Vedic Times: Simulations using Planetarium software”, Proc. International Conference on Indian Sciences in the pre-Adisankara Period, Dec 14, 2007, Hyderabad, India,pp 69-101.

## Book Chapters

B. N. Narahari Achar

"Date of the Mahabharata War Based on Simulations using Planetarium Software" in
The Date of the Mahabharata War Based on Astronomical Data Edited by Suryakanth U.
Kamath, The Mythic Society, Bangalore, India, (2004) pp. 65-115

B. N. Narahari Achar

"Planetarium Software and the Date of the Mahabharata War" in The Mahabharata: What
is not here is nowhere else, Edited by T. S. Rukmani, Munshiram Manoharlal Publishers,
New Delhi, India (2005), Pp. 247-263

B. N. Narahari Achar

"Planetary Configurations in the Epic Mahabharata: Revisiting an Exercise in Archaeoastronomy"
in Viewing the Sky Through Past and Present Cultures: Proceedings of the Oxford VII
International Conference on Archaeoastronomy, Edited by Todd W. Boswick and Byran
Bates, City of Phoenix Parks and Recreation Department (2006), pp 433-449.

B. N. Narahari Achar

The Mahabharata War: It's Date on the basis of Astronomical References in

Origin of Indian Civilization, Edited by Bal Ram Singh, D K Print World , New Delhi,
India (2010), Pp. 202-252

B. N. Narahari Achar

Revised Chronology of the Vedic People in Origins of Civilization, edited by Sureshwar
D Sinha and B. R. Mani

Bharatiya Kala Prakashan, Delhi, India, (2011), pp 69-96

B. N. Narahari Achar and John W. Hanneken,

Microscopic Formulation of Fractional Theory of Viscoelasticity”, in Viscoelasticity – From Theory to Biological Applications, edited by Juan de Vicente (Ed), Intech Publishing, NY, (2012) ISBN: 978-953-51-0841-2 http://dx.doi.org/10.5772/51493

B. N. Narahari Achar

Rgveda Its Chronology on the basis of Astronomical References in

Perspectives on the Origin of Indian Civilization, edited by Angela Marcantonio and
Girish Nath Jha, Center for Indic Studies, Dartmouth MA and D K Print world, New Delhi,
India,(2013), pp 155-192 .