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BIGEOMETRIC INTEGRAL CALCULUS

Year 2018, Volume: 8 Issue: 2, 374 - 385, 01.12.2018

Abstract

Objective of this paper is to discuss about the properties of inde nite and de nite bigeometric integration. We also discuss about some applications of bigeometric integration.

References

  • [1] Bashirov A. E., Rıza M., (2011), On Complex multiplicative differentiation, TWMS J. App. Eng. Math. 1(1) 75-85.
  • [2] Bashirov A. E., Mısırlı E., Tandoˇgdu Y., Ozyapıcı A., (2011), On modeling with multiplicative differ- ¨ ential equations, Appl. Math. J. Chinese Uni. 26(4)425-438.
  • [3] Bashirov A. E., Kurpınar E. M., Ozyapici A., (2008), Multiplicative Calculus and its applications, J. ¨ Math. Anal. Appl. 337 p.36-48.
  • [4] Boruah K., Hazarika B., (2016), Application of geometric calculus in numerical analysis and difference sequence spaces, J. Math. Anal. Appl. doi:10.1016/j.jmaa.2016.12.066
  • [5] Boruah K., Hazarika B., (2016), Some basic properties of G-calculus and its applications in numerical analysis, arXiv:1607.07749v1.
  • [6] Boruah K., Hazarika B., (2016), G-calculus, ariXv:1608.08088v2.
  • [7] Boruah K., Hazarika B., Solution of bigeometric-differential equations by numerical methods, preprint.
  • [8] C¸ akmak A. F., Ba¸sar F., (2012), On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. Article ID 932734, p.12.
  • [9] C¸ akmak A. F., Ba¸sar F., (2014), Certain spaces of functions over the field of non-Newtonian complex numbers, Abstr. Appl. Anal., Article ID 236124, p.12.
  • [10] C¸ akmak A. F., Ba¸sar F., (2014), On line and double integrals in the non-Newtonian sense, AIP Conference Proceedings, 1611, p.415-423.
  • [11] C¸ akmak A. F., Ba¸sar F., (2014), Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. 6(1), p.27-37.
  • [12] Campbell D., Multiplicative Calculus and Student Projects, Department of Mathematical Sciences, United States Military Academy, West Point, NY,10996, USA.
  • [13] Coco M., Multiplicative Calculus, Lynchburg College.
  • [14] Grossman M., (1983), Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts.
  • [15] Grossman M., Katz R., (1972), Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts.
  • [16] Grossman J., Grossman J., Katz R., (1980), The First Systems of Weighted Differential and Integral Calculus, University of Michigan.
  • [17] Grossman J., (1981), Meta-Calculus: Differential and Integral, University of Michigan.
  • [18] Grossman J., Katz R., (1983), Averages, A new Approach, University of Michigan.
  • [19] Grossman M., (1979), The First Nonlinear System of Differential and Integral Calculus University of California.
  • [20] Kadak U., ”Ozl¨uk M., (2015), Generalized Runge-Kutta method with respect to non-Newtonian calculus, Abst. Appl. Anal., Article ID 594685, p.10
  • [21] C´ordova-Lepe F., (2006), The multiplicative derivative as a measure of elasticity in economics, TMAT Revista Latinoamericana de Ciencias e Ingener´ıria, 2(3), p.8.
  • [22] Spivey M. Z., A Product Calculus, University of Puget Sound, Tacoma, Washington 98416-1043.
  • [23] Stanley D., (1999), A multiplicative calculus, Primus IX 4, 310-326.
  • [24] Tekin S., Ba¸sar F., (2013), Certain sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal., Article ID 739319, doi: 10.1155/2013/ 739319.
  • [25] T¨urkmen C., Ba¸sar F., (2012), Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1 61(2) p.17-34.
  • [26] Uzer A., (2010), Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. 60, p.2725-2737.
Year 2018, Volume: 8 Issue: 2, 374 - 385, 01.12.2018

Abstract

References

  • [1] Bashirov A. E., Rıza M., (2011), On Complex multiplicative differentiation, TWMS J. App. Eng. Math. 1(1) 75-85.
  • [2] Bashirov A. E., Mısırlı E., Tandoˇgdu Y., Ozyapıcı A., (2011), On modeling with multiplicative differ- ¨ ential equations, Appl. Math. J. Chinese Uni. 26(4)425-438.
  • [3] Bashirov A. E., Kurpınar E. M., Ozyapici A., (2008), Multiplicative Calculus and its applications, J. ¨ Math. Anal. Appl. 337 p.36-48.
  • [4] Boruah K., Hazarika B., (2016), Application of geometric calculus in numerical analysis and difference sequence spaces, J. Math. Anal. Appl. doi:10.1016/j.jmaa.2016.12.066
  • [5] Boruah K., Hazarika B., (2016), Some basic properties of G-calculus and its applications in numerical analysis, arXiv:1607.07749v1.
  • [6] Boruah K., Hazarika B., (2016), G-calculus, ariXv:1608.08088v2.
  • [7] Boruah K., Hazarika B., Solution of bigeometric-differential equations by numerical methods, preprint.
  • [8] C¸ akmak A. F., Ba¸sar F., (2012), On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. Article ID 932734, p.12.
  • [9] C¸ akmak A. F., Ba¸sar F., (2014), Certain spaces of functions over the field of non-Newtonian complex numbers, Abstr. Appl. Anal., Article ID 236124, p.12.
  • [10] C¸ akmak A. F., Ba¸sar F., (2014), On line and double integrals in the non-Newtonian sense, AIP Conference Proceedings, 1611, p.415-423.
  • [11] C¸ akmak A. F., Ba¸sar F., (2014), Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. 6(1), p.27-37.
  • [12] Campbell D., Multiplicative Calculus and Student Projects, Department of Mathematical Sciences, United States Military Academy, West Point, NY,10996, USA.
  • [13] Coco M., Multiplicative Calculus, Lynchburg College.
  • [14] Grossman M., (1983), Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts.
  • [15] Grossman M., Katz R., (1972), Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts.
  • [16] Grossman J., Grossman J., Katz R., (1980), The First Systems of Weighted Differential and Integral Calculus, University of Michigan.
  • [17] Grossman J., (1981), Meta-Calculus: Differential and Integral, University of Michigan.
  • [18] Grossman J., Katz R., (1983), Averages, A new Approach, University of Michigan.
  • [19] Grossman M., (1979), The First Nonlinear System of Differential and Integral Calculus University of California.
  • [20] Kadak U., ”Ozl¨uk M., (2015), Generalized Runge-Kutta method with respect to non-Newtonian calculus, Abst. Appl. Anal., Article ID 594685, p.10
  • [21] C´ordova-Lepe F., (2006), The multiplicative derivative as a measure of elasticity in economics, TMAT Revista Latinoamericana de Ciencias e Ingener´ıria, 2(3), p.8.
  • [22] Spivey M. Z., A Product Calculus, University of Puget Sound, Tacoma, Washington 98416-1043.
  • [23] Stanley D., (1999), A multiplicative calculus, Primus IX 4, 310-326.
  • [24] Tekin S., Ba¸sar F., (2013), Certain sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal., Article ID 739319, doi: 10.1155/2013/ 739319.
  • [25] T¨urkmen C., Ba¸sar F., (2012), Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1 61(2) p.17-34.
  • [26] Uzer A., (2010), Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. 60, p.2725-2737.
There are 26 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

K. Boruah This is me

B. Hazarika This is me

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

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