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BG-Volterra İntegral Denklemleri ve BG-Diferansiyel Denklemlerle İlişkisi

Year 2020, Volume: 10 Issue: 3, 814 - 829, 15.07.2020
https://doi.org/10.17714/gumusfenbil.709376

Abstract

Bu çalışmada,
bigeometrik integral yardımıyla bigeometrik Volterra integral denklemleri
tanımlanmıştır. Çalışmanın asıl amacı bigeometrik manada Volterra integral
denklemleri ile bigeometrik manada diferansiyel denklemler arasındaki ilişkiyi
araştırmaktır. 

References

  • Aniszewska, D. and Rybaczuk, M., 2005. Analysis of the Multiplicative Lorenz System. Chaos Solitons Fractals, 25, 79–90.
  • Boruah, K. and Hazarika, B., 2018a. -Calculus. TWMS J. Pure Appl. Math., 8(1), 94-105.
  • Boruah, K. and Hazarika, B., 2018b. Bigeometric Integral Calculus. TWMS J. Pure Appl. Math., 8(2), 374-385.
  • Boruah, K., Hazarika, B. and Bashirov, A.E., 2018. Solvability of Bigeometric Diferrential Equations by Numerical Methods. Bol. Soc. Parana. Mat., doi: 10.5269/bspm.39444.
  • Brunner, H., 2017. Volterra Integral Equations: An Introduction to Theory and Applications, Cambridge University Press, 387p.
  • Córdova-Lepe, F. 2015. The Multiplicative Derivative as a Measure of Elasticity in Economics. TEMAT-Theaeteto Antheniensi Mathematica, 2(3), online.
  • Çakmak, A.F. and Başar, F., 2012. Some New Results on Sequence Spaces with respect to Non-Newtonian Calculus. J. Inequal. Appl., 228(1).
  • Çakmak, A.F. and Başar, F., 2014a. On Line and Double Integrals in the Non-Newtonian Sense. AIP Conference Proceedings, 1611, 415-423.
  • Çakmak, A.F. and Başar, F., 2014b. Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers. Abstr. Appl. Anal., Article ID 236124, 12 pages, doi:10.1155/2014/236124.
  • Çakmak, A.F. and Başar, F., 2015. Some Sequence Spaces and Matrix Transformations in Multiplicative sense. TWMS J. Pure Appl. Math.,6 (1), 27-37.
  • Duyar, C. and Oğur, O., 2017. A Note on Topology of Non-Newtonian Real Numbers. IOSR Journal of Mathematics, 13(6), 11-14.
  • Duyar, C and Sağır, B., 2017. Non-Newtonian Comment of Lebesgue Measure in Real Numbers. J. Math, Article ID 6507013.
  • Erdoğan, M. and Duyar, C., 2018. Non-Newtonian Improper Integrals. Journal of Science and Arts, 1(42), 49-74.
  • Güngör, N., 2020. Some Geometric of The Non-Newtonian Sequence Spaces . Math. Slovaca, 70 (3), 689-696.
  • Grosmann, M. and Katz R., 1972. Non-Newtonian Calculus, Lee Press, Pigeon Cove Massachussets, 94p.
  • Grosmann, M. 1979. An Introduction to Non-Newtonian Calculus. International Journal of Mathematical Education in Science and Technology,10(4), 525-528.
  • Grosmann, M., 1983. Bigeometric Calculus: A system with a Scale Free Derivative, 1st ed., Archimedes Foundation, Rockport Massachussets, 100p.
  • Kadak, U. and Özlük, M., 2014. Generalized Runge-Kutta Methods with Respect to Non-Newtonian Calculus. Abstr. Appl. Anal., Article ID 594685.
  • Krasnov, M., Kiselev, K. and Makarenko, G., 1971. Problems and Exercises in Integral Equation, Mır Publishers, Moscow, 214p.
  • Maturi, D.A., 2019. The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple. Advances in Pure Mathematics, 9, 832-843.
  • Rybaczuk, M. and Stoppel, P., 2000. The fractal growth of fatigue defects in materials. International Journal of Fracture, 103, 71–94.
  • Sağır, B. and Erdoğan, F., 2019. On the Function Sequences and Series in the Non-Newtonian Calculus. Journal of Science and Arts, 4(49), 915-936.
  • Smithies, F., 1958. Integral Equations, Cambridge University Press, London, 172p.
  • Tekin, S. and Başar, F., 2013. Certain Sequence Spaces over the Non-Newtonian Complex Field. Abstr. Appl. Anal. 2013, Article ID 739319, 11 pages, doi: 10.1155/2013/ 739319.
  • Türkmen, C. and Başar, F., 2012a. Some Basic Results on the Sets of Sequences with Geometric Calculus. AIP Conference Proceedings, 1470, 95-98.
  • Türkmen, C. and Başar, F., 2012b. Some Results on the Sets of Sequences with Geometric Calculus. Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 61(2), 17-34.
  • Volterra, V. and Hostinsky, B. 1938. Opérations Infinitésimales linéares, Herman, Paris.
  • Zarnan, J.A., 2016. Numerical Solution of Volterra Integral Equations of Second Kind, Int. J. Comput. Sci. Mobile Comput., 5(7), 509-517.

BG-Volterra Integral Equations and Relationship with BG-Differential Equations

Year 2020, Volume: 10 Issue: 3, 814 - 829, 15.07.2020
https://doi.org/10.17714/gumusfenbil.709376

Abstract

In this study, the Volterra
integral equations are defined in the sense of bigeometric calculus by the aid
of bigeometric integral.  The main aim of
the study is to research the relationship between bigeometric Volterra integral
equations and bigeometric differential equations.

References

  • Aniszewska, D. and Rybaczuk, M., 2005. Analysis of the Multiplicative Lorenz System. Chaos Solitons Fractals, 25, 79–90.
  • Boruah, K. and Hazarika, B., 2018a. -Calculus. TWMS J. Pure Appl. Math., 8(1), 94-105.
  • Boruah, K. and Hazarika, B., 2018b. Bigeometric Integral Calculus. TWMS J. Pure Appl. Math., 8(2), 374-385.
  • Boruah, K., Hazarika, B. and Bashirov, A.E., 2018. Solvability of Bigeometric Diferrential Equations by Numerical Methods. Bol. Soc. Parana. Mat., doi: 10.5269/bspm.39444.
  • Brunner, H., 2017. Volterra Integral Equations: An Introduction to Theory and Applications, Cambridge University Press, 387p.
  • Córdova-Lepe, F. 2015. The Multiplicative Derivative as a Measure of Elasticity in Economics. TEMAT-Theaeteto Antheniensi Mathematica, 2(3), online.
  • Çakmak, A.F. and Başar, F., 2012. Some New Results on Sequence Spaces with respect to Non-Newtonian Calculus. J. Inequal. Appl., 228(1).
  • Çakmak, A.F. and Başar, F., 2014a. On Line and Double Integrals in the Non-Newtonian Sense. AIP Conference Proceedings, 1611, 415-423.
  • Çakmak, A.F. and Başar, F., 2014b. Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers. Abstr. Appl. Anal., Article ID 236124, 12 pages, doi:10.1155/2014/236124.
  • Çakmak, A.F. and Başar, F., 2015. Some Sequence Spaces and Matrix Transformations in Multiplicative sense. TWMS J. Pure Appl. Math.,6 (1), 27-37.
  • Duyar, C. and Oğur, O., 2017. A Note on Topology of Non-Newtonian Real Numbers. IOSR Journal of Mathematics, 13(6), 11-14.
  • Duyar, C and Sağır, B., 2017. Non-Newtonian Comment of Lebesgue Measure in Real Numbers. J. Math, Article ID 6507013.
  • Erdoğan, M. and Duyar, C., 2018. Non-Newtonian Improper Integrals. Journal of Science and Arts, 1(42), 49-74.
  • Güngör, N., 2020. Some Geometric of The Non-Newtonian Sequence Spaces . Math. Slovaca, 70 (3), 689-696.
  • Grosmann, M. and Katz R., 1972. Non-Newtonian Calculus, Lee Press, Pigeon Cove Massachussets, 94p.
  • Grosmann, M. 1979. An Introduction to Non-Newtonian Calculus. International Journal of Mathematical Education in Science and Technology,10(4), 525-528.
  • Grosmann, M., 1983. Bigeometric Calculus: A system with a Scale Free Derivative, 1st ed., Archimedes Foundation, Rockport Massachussets, 100p.
  • Kadak, U. and Özlük, M., 2014. Generalized Runge-Kutta Methods with Respect to Non-Newtonian Calculus. Abstr. Appl. Anal., Article ID 594685.
  • Krasnov, M., Kiselev, K. and Makarenko, G., 1971. Problems and Exercises in Integral Equation, Mır Publishers, Moscow, 214p.
  • Maturi, D.A., 2019. The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple. Advances in Pure Mathematics, 9, 832-843.
  • Rybaczuk, M. and Stoppel, P., 2000. The fractal growth of fatigue defects in materials. International Journal of Fracture, 103, 71–94.
  • Sağır, B. and Erdoğan, F., 2019. On the Function Sequences and Series in the Non-Newtonian Calculus. Journal of Science and Arts, 4(49), 915-936.
  • Smithies, F., 1958. Integral Equations, Cambridge University Press, London, 172p.
  • Tekin, S. and Başar, F., 2013. Certain Sequence Spaces over the Non-Newtonian Complex Field. Abstr. Appl. Anal. 2013, Article ID 739319, 11 pages, doi: 10.1155/2013/ 739319.
  • Türkmen, C. and Başar, F., 2012a. Some Basic Results on the Sets of Sequences with Geometric Calculus. AIP Conference Proceedings, 1470, 95-98.
  • Türkmen, C. and Başar, F., 2012b. Some Results on the Sets of Sequences with Geometric Calculus. Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 61(2), 17-34.
  • Volterra, V. and Hostinsky, B. 1938. Opérations Infinitésimales linéares, Herman, Paris.
  • Zarnan, J.A., 2016. Numerical Solution of Volterra Integral Equations of Second Kind, Int. J. Comput. Sci. Mobile Comput., 5(7), 509-517.
There are 28 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nihan Güngör 0000-0003-1235-2700

Publication Date July 15, 2020
Submission Date March 25, 2020
Acceptance Date June 23, 2020
Published in Issue Year 2020 Volume: 10 Issue: 3

Cite

APA Güngör, N. (2020). BG-Volterra Integral Equations and Relationship with BG-Differential Equations. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(3), 814-829. https://doi.org/10.17714/gumusfenbil.709376