Research Article
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A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS

Year 2024, , 73 - 85, 29.12.2024
https://doi.org/10.33773/jum.1552823

Abstract

The paper deals with the non-homogeneous boundary value problems established in the multiplicative calculus. For this problem, the multiplicative meanings of concepts such as adjoint operator, self-adjoint operator, Lagrange identity, Green's formula are obtained. Then, a criterion is given for the existence of solutions to non-homogeneous multiplicative boundary value problems.

References

  • M. E. Aydin, A. Has, B. Yilmaz, A Non-Newtonian Approach İn Differential Geometry Of Curves: Multiplicative Rectifying Curves, Bulletin of the Korean Mathematical Society, Vol.61, No.3, pp.849-866 (2024).
  • A. Bal, N. Yalcin, M. Dedeturk, Solutions of Multiplicative Integral Equations Via The Multiplicative Power Series Method, Politeknik Dergisi, Vol.26, No.1, pp.311-320 (2023).
  • J. S. Bardi, The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time. New York: Thunder's Mouth Press, İSBN 1-56025-706-7 (2006).
  • A. Bashirov, E. M. Kurpinar, A. Ozyapici, Multiplicative Calculus and İts Applications, Journal of Mathematical Analysis and Applications, Vol.337, No.1, pp.36-48 (2008).
  • A. Bashirov, G. Bashirova, Dynamics of Literary Texts and Diffusion, Online Journal of Communication and Media Technologies, Vol.1, No.3, pp.60-82 (2011).
  • A. Bashirov, E. Misirli, Y. Tandogdu, A. Ozyapici, On Modeling with Multiplicative Differential Equations, Applied Mathematics-A Journal of Chinese Universities, Vol.26, No.4, pp.425-438 (2011).
  • B. Bilgehan, A. Ozyapici, Z. Hammouch, Y. Gurefe, Predicting the Spread of COVİD-19 with a Machine Learning Technique and Multiplicative Calculus, Soft Computing, Vol.26, No.16, pp.8017-8024 (2022).
  • C. B. Boyer, The History of the Calculus and its Conceptual Development, New York: Dover. OCLC 643872 (1959).
  • D. Campbell, Multiplicative Calculus and Student Projects, Projects, Problems, Resources and İssues in Mathematics Undergraduate Studies, Vol.9, No.4, pp.327-332 (1999).
  • F. Cordova-Lepe, The Multiplicative Derivative As a Measure of Elasticity in Economics, Theaeteto Atheniensi Mathematica, Vol.2 (2006).
  • D. Filip, C. Piatecki, A Non-Newtonian Examination of The Theory of Exogenous Economic Growth, Mathematica Aeterna, Vol.10 (2014).
  • D. Filip, C. Piatecki, In defense of a non-newtonian economic analysis. (2014).
  • L. Florack, H. Van Assen, Multiplicative Calculus in Biomedical İmage Analysis, Journal of Mathematical İmaging and Vision, Vol.42, pp.64-75 (2012).
  • S. Goktas, A New Type of Sturm‐Liouville Equation in the Non Newtonian Calculus, Journal of Function Spaces, Vol.2021, No.1, pp.1-8 (2021).
  • M. Grossman, R. Katz, Non-Newtonian Calculus. Pigeon Cove, Massachusetts. (1972)
  • M. Grossman, An introduction to non Newtonian calculus, International Journal of Mathematical Educational in Science and Technology, Vol.10, No.4, pp.525-528 (1979).
  • A. Has, B. Yilmaz, A non-Newtonian Conics in Multiplicative Analytic Geometry, Turkish Journal of Mathematics, Vol.48, No.5, pp.976-994 (2024).
  • A. Has, B. Yilmaz, H. Yildirim, A Non-Newtonian Magnetic Curves in Multiplicative Riemann Manifolds, Physica Scripta, Vol.99, No.4, 045239 (2024).
  • L. D. Hoffmann, G. L. Bradley , Calculus for Business, Economics, and the Social and Life Sciences (8th ed.). Boston: McGraw Hill (2004).
  • U. Kadak, H. Efe , The Construction of Hilbert Spaces over the Non-Newtonian Field, İnternational Journal of Analysis, pp.1-10. (2014).
  • E. Misirli, Y. Gurefe , Multiplicative Adams Bashforth-Moulton Methods, Numerical Algorithms, Vol.57, pp.425-439 (2011).
  • E. Misirli, A. Ozyapici , Exponential Approximations On Multiplicative Calculus, İn Proc. Jangjeon Math. Soc, Vol.12, No.2, pp.227-236 (2009).
  • G. B. Oznur, G. G. Ozbey, Y. Aygar Kucukevcilioglu, R. Aktas Karaman, A Study Of The Scattering Analysis of the Multiplicative Sturm-Liouville Problem, Turkish Journal of Mathematics, Vol.48, No.3, pp.608-622 (2024).
  • D. Stanley, A Multiplicative Calculus, Problems, Resources and İssues in Mathematics Undergraduate Studies, Vol.9, pp.310-326 (1999)
  • N. Yalcin, The Solutions Of Multiplicative Hermite Differential Equation And Multiplicative Hermite Polynomials, Rendiconti del Circolo Matematico di Palermo Series 2, Vol.70, No.1, pp.9-21 (2021).
  • Multiplicative Chebyshev Differential Equations and Multiplicative Chebyshev Polynomials, Thermal Science, Vol.26, No.Spec. issue 2, pp.785-799 (2022).
  • N. Yalcin, E. Celik, A. Gokdogan , Multiplicative Laplace Transform and its Applications, Optik, Elsevier GmbH. 127, pp.9984-9995 (2016).
  • N. Yalcin, E. Celik, Solution of Multiplicative Homogeneous Linear Differential Equations with Constant Exponentials, New Trends in Mathematical Sciences, Vol.6, No.2, pp.58-67 (2018).
Year 2024, , 73 - 85, 29.12.2024
https://doi.org/10.33773/jum.1552823

Abstract

References

  • M. E. Aydin, A. Has, B. Yilmaz, A Non-Newtonian Approach İn Differential Geometry Of Curves: Multiplicative Rectifying Curves, Bulletin of the Korean Mathematical Society, Vol.61, No.3, pp.849-866 (2024).
  • A. Bal, N. Yalcin, M. Dedeturk, Solutions of Multiplicative Integral Equations Via The Multiplicative Power Series Method, Politeknik Dergisi, Vol.26, No.1, pp.311-320 (2023).
  • J. S. Bardi, The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time. New York: Thunder's Mouth Press, İSBN 1-56025-706-7 (2006).
  • A. Bashirov, E. M. Kurpinar, A. Ozyapici, Multiplicative Calculus and İts Applications, Journal of Mathematical Analysis and Applications, Vol.337, No.1, pp.36-48 (2008).
  • A. Bashirov, G. Bashirova, Dynamics of Literary Texts and Diffusion, Online Journal of Communication and Media Technologies, Vol.1, No.3, pp.60-82 (2011).
  • A. Bashirov, E. Misirli, Y. Tandogdu, A. Ozyapici, On Modeling with Multiplicative Differential Equations, Applied Mathematics-A Journal of Chinese Universities, Vol.26, No.4, pp.425-438 (2011).
  • B. Bilgehan, A. Ozyapici, Z. Hammouch, Y. Gurefe, Predicting the Spread of COVİD-19 with a Machine Learning Technique and Multiplicative Calculus, Soft Computing, Vol.26, No.16, pp.8017-8024 (2022).
  • C. B. Boyer, The History of the Calculus and its Conceptual Development, New York: Dover. OCLC 643872 (1959).
  • D. Campbell, Multiplicative Calculus and Student Projects, Projects, Problems, Resources and İssues in Mathematics Undergraduate Studies, Vol.9, No.4, pp.327-332 (1999).
  • F. Cordova-Lepe, The Multiplicative Derivative As a Measure of Elasticity in Economics, Theaeteto Atheniensi Mathematica, Vol.2 (2006).
  • D. Filip, C. Piatecki, A Non-Newtonian Examination of The Theory of Exogenous Economic Growth, Mathematica Aeterna, Vol.10 (2014).
  • D. Filip, C. Piatecki, In defense of a non-newtonian economic analysis. (2014).
  • L. Florack, H. Van Assen, Multiplicative Calculus in Biomedical İmage Analysis, Journal of Mathematical İmaging and Vision, Vol.42, pp.64-75 (2012).
  • S. Goktas, A New Type of Sturm‐Liouville Equation in the Non Newtonian Calculus, Journal of Function Spaces, Vol.2021, No.1, pp.1-8 (2021).
  • M. Grossman, R. Katz, Non-Newtonian Calculus. Pigeon Cove, Massachusetts. (1972)
  • M. Grossman, An introduction to non Newtonian calculus, International Journal of Mathematical Educational in Science and Technology, Vol.10, No.4, pp.525-528 (1979).
  • A. Has, B. Yilmaz, A non-Newtonian Conics in Multiplicative Analytic Geometry, Turkish Journal of Mathematics, Vol.48, No.5, pp.976-994 (2024).
  • A. Has, B. Yilmaz, H. Yildirim, A Non-Newtonian Magnetic Curves in Multiplicative Riemann Manifolds, Physica Scripta, Vol.99, No.4, 045239 (2024).
  • L. D. Hoffmann, G. L. Bradley , Calculus for Business, Economics, and the Social and Life Sciences (8th ed.). Boston: McGraw Hill (2004).
  • U. Kadak, H. Efe , The Construction of Hilbert Spaces over the Non-Newtonian Field, İnternational Journal of Analysis, pp.1-10. (2014).
  • E. Misirli, Y. Gurefe , Multiplicative Adams Bashforth-Moulton Methods, Numerical Algorithms, Vol.57, pp.425-439 (2011).
  • E. Misirli, A. Ozyapici , Exponential Approximations On Multiplicative Calculus, İn Proc. Jangjeon Math. Soc, Vol.12, No.2, pp.227-236 (2009).
  • G. B. Oznur, G. G. Ozbey, Y. Aygar Kucukevcilioglu, R. Aktas Karaman, A Study Of The Scattering Analysis of the Multiplicative Sturm-Liouville Problem, Turkish Journal of Mathematics, Vol.48, No.3, pp.608-622 (2024).
  • D. Stanley, A Multiplicative Calculus, Problems, Resources and İssues in Mathematics Undergraduate Studies, Vol.9, pp.310-326 (1999)
  • N. Yalcin, The Solutions Of Multiplicative Hermite Differential Equation And Multiplicative Hermite Polynomials, Rendiconti del Circolo Matematico di Palermo Series 2, Vol.70, No.1, pp.9-21 (2021).
  • Multiplicative Chebyshev Differential Equations and Multiplicative Chebyshev Polynomials, Thermal Science, Vol.26, No.Spec. issue 2, pp.785-799 (2022).
  • N. Yalcin, E. Celik, A. Gokdogan , Multiplicative Laplace Transform and its Applications, Optik, Elsevier GmbH. 127, pp.9984-9995 (2016).
  • N. Yalcin, E. Celik, Solution of Multiplicative Homogeneous Linear Differential Equations with Constant Exponentials, New Trends in Mathematical Sciences, Vol.6, No.2, pp.58-67 (2018).
There are 28 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems
Journal Section Research Article
Authors

Sertaç Göktaş 0000-0001-7842-6309

Ayşenur Kale 0000-0001-5458-6463

Aslı Öner 0000-0002-4799-9574

Yusuf Gürefe 0000-0002-7210-5683

Publication Date December 29, 2024
Submission Date September 19, 2024
Acceptance Date November 2, 2024
Published in Issue Year 2024

Cite

APA Göktaş, S., Kale, A., Öner, A., Gürefe, Y. (2024). A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS. Journal of Universal Mathematics, 7(To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"), 73-85. https://doi.org/10.33773/jum.1552823
AMA Göktaş S, Kale A, Öner A, Gürefe Y. A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS. JUM. December 2024;7(To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"):73-85. doi:10.33773/jum.1552823
Chicago Göktaş, Sertaç, Ayşenur Kale, Aslı Öner, and Yusuf Gürefe. “A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS”. Journal of Universal Mathematics 7, no. To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" (December 2024): 73-85. https://doi.org/10.33773/jum.1552823.
EndNote Göktaş S, Kale A, Öner A, Gürefe Y (December 1, 2024) A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS. Journal of Universal Mathematics 7 To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" 73–85.
IEEE S. Göktaş, A. Kale, A. Öner, and Y. Gürefe, “A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS”, JUM, vol. 7, no. To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", pp. 73–85, 2024, doi: 10.33773/jum.1552823.
ISNAD Göktaş, Sertaç et al. “A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS”. Journal of Universal Mathematics 7/To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" (December 2024), 73-85. https://doi.org/10.33773/jum.1552823.
JAMA Göktaş S, Kale A, Öner A, Gürefe Y. A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS. JUM. 2024;7:73–85.
MLA Göktaş, Sertaç et al. “A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS”. Journal of Universal Mathematics, vol. 7, no. To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 2024, pp. 73-85, doi:10.33773/jum.1552823.
Vancouver Göktaş S, Kale A, Öner A, Gürefe Y. A STUDY ON NON-HOMOGENEOUS MULTIPLICATIVE BOUNDARY VALUE PROBLEMS. JUM. 2024;7(To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"):73-85.