Properties of Modified Double Laplace Transforms and Special Functions

Authors

  • V. K. Borawake Department of Mathematics, Sinhgad Technical Education Society’s Smt. Kashibai Navale College of Engineering (affiliated to Savitribai Phule Pune University), Vadgaon (Budruk), Pune 411041, Maharashtra, India https://orcid.org/0009-0005-4613-6696
  • A. P. Hiwarekar Department of Mathematics, Vidya Pratishthan’s Kamalnayan Bajaj Institute of Engineering and Technology (affiliated to Savitribai Phule Pune University), Baramati 413133, Pune, Maharashtra, India https://orcid.org/0000-0003-2070-4534

DOI:

https://doi.org/10.26713/cma.v15i2.2765

Keywords:

Laplace transform, Multiple integral transforms, Integral transform of special functions, Double Laplace transform, Convolution

Abstract

This paper deals with new results on modified double Laplace transforms and special functions. Starting with basic definitions and results, we have obtained a modified double Laplace transform of unit step functions, and periodic functions and developed new theorems. Finally, we illustrate our results with examples.

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References

A. Ali, Abdullah and A. Ahmad, The solution of Poisson partial differential equations via Double Laplace Transform Method, Partial Differential Equations in Applied Mathematics 4 (2021) 100058, DOI: 10.1155/2013/932578.

N. S. Amberkhane, S. P. Hatkar and K. L. Bondar, Exponential transform of some special functions, International Journal of Mathematics Trends and Technology 68(6) (2022), 54 – 59, DOI: 10.14445/22315373/IJMTT-V68I6P506.

V. K. Borawake and A. P. Hiwarekar, Modified double Laplace transform of partial derivatives and its applications, Gulf Journal of Mathematics 16(2) (2024), 353 – 363, DOI: 10.56947/gjom.v16i2.1892.

V. K. Borawake and A. P. Hiwarekar, New results on the modified double Laplace transform and its properties, Journal of the Maharaja Sayajirao University of Baroda 57(VII) (2023), 61 – 66.

K.-S. Chiu and T. Li, Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments, Mathematische Nachrichten 292(10) (2019), 2153 – 2164, DOI: 10.1002/mana.201800053.

W. S. Chung, T. Kim and H. I. Know, On the q-analog of the Laplace transform, Russian Journal of Mathematical Physics 21 (2014), 156 – 168, DOI: 10.1134/S1061920814020034.

A. Daci and S. Tola, Application of Laplace transform in Finance, Mathematical Modeling 2(4) (2018), 130 – 133, URL: https://stumejournals.com/journals/mm/2018/4/130.

A. Daci and S. Tola, Laplace transform, application in population growth, International Journal of Recent Technology and Engineering 8(2) (2019), 954 – 957, DOI: 10.35940/ijrte.B1189.0782S419.

L. Debnath and D. Bhatta, Integral Transform and Their Applications, 2nd edition, Chapman and Hall/CRC, New York, 728 pages (2006), DOI: 10.1201/9781420010916.

L. Debnath, The double Laplace transforms and their properties with applications to functional, integral and partial differential equations, International Journal of Applied and Computational Mathematics 2 (2016), 223 – 241, DOI: 10.1007/s40819-015-0057-3.

R. R. Dhunde and G. L. Waghmare, Double Laplace transform method in mathematical physics, International Journal of Theoretical and Mathematics Physics 7(1) (2017), 14 – 20, DOI: 10.5923/j.ijtmp.20170701.04.

R. R. Dhunde, N. M. Bhonde and P. R. Dhongle, Some remarks on the properties of double Laplace transforms, International Journal of Applied Physics and Mathematics 3(4) (2013), 293 – 295, DOI: 10.7763/IJAPM.2013.V3.224.

H. Eltayeb and A. Kiliçman, A note on double Laplace transform and telegraphic equations, Abstract and Applied Analysis 2023(1) (2013), 932578, DOI: 10.1155/2013/932578.

H. Eltayeb and A. Kiliçman, A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform, Applied Mathematics Letters 21(12) (2008), 1324 – 1329, DOI: 10.1016/j.aml.2007.12.028.

H. Eltayeb and A. Kiliçman, On double Sumudu transform and double Laplace transform, Malaysian Journal of Mathematical Sciences 4(1) (2010), 17 – 30, DOI: 10.1134/S1995080209030044.

A. P. Hiwarekar, Extension of prefunctions and its relation with Mittag-Leffler function, The Journal of Analysis 28 (2020), 169 – 177, DOI: 10.1007/s41478-017-0052-7.

A. P. Hiwarekar, New mathematical modeling for cryptography, Journal of Information Assurance and Security 9 (2014), 27 – 33, URL: http://www.mirlabs.org/jias/secured/Volume9-Issue1/Paper4.pdf.

A. P. Hiwarekar, Triple Laplace transforms and its properties, Advances and Applications in Mathematical Sciences 20(11) (2021), 2843 – 2851.

T. Kim and D. S. Kim, Degenerate Laplace transform and degenerate gamma function, Russian Journal of Mathematical Physics 24 (2017), 241 – 248, DOI: 10.1134/S1061920817020091.

Y. J. Kim, B. M. Kim, L.-C. Jang and J. Kwon, A note on modified degenerate gamma and Laplace transformation, Symmetry 10(10) (2018), 471, DOI: 10.3390/sym10100471.

N. Kokulan and C. H. Lai, A Laplace transform method for the image in-painting, in: 12th International Symposium on Distributed Computing and Applications to Business, Engineering & Science (Kingston upon Thames, UK, 2013), pp. 243 – 246, DOI: 10.1109/DCABES.2013.51.

G. V. Nozhak and A. A. Paskar, Application of a modified discrete Laplace transform to finding processes in certain hyperbolic system with distributed parameters (Russian), Mathematical Methods in Mechanics. Mat. Issled 57 (1980), 83 – 90.

S.-L. Nyeo and R. R. Ansari, Space Bayesian learning for the Laplace transform inversion in dynamic light scattering, Journal of Computational and Applied Mathematics 235(8) (2011), 2861 – 2872, DOI: 10.1016/j.cam.2010.12.008.

A. D. Poularikas and S. Seely, Laplace transform, Chapter 5, in The Transforms and Applications Handbook, 2nd edition, Boka Raton, CRC Press LLC, (2000), URL: https://dsp-book.narod.ru/TAH/ch05.pdf.

E. J. Riekstyn’s, On certain possibilities of solution of a system of telegraph equations using the Laplace transform in the case of a composite conductor (Russian), Latvijas Valsts Univ. Zinatn. Raksti 8 (1956), 49 – 53.

M. Saif, F. Khan, K. S. Nisar and S. Araci, Modified Laplace transform and its properties, Journal of Mathematics and Computer Science 21(2) (2020), 127 – 135, DOI: 10.22436/jmcs.021.02.04.

J. L. Schiff, The Laplace Transform: Theory and Applications, Springer, New York, xiv + 236 pages (1999), DOI: 10.1007/978-0-387-22757-3.

G.-Y. Tsaur and J. Wang, Close connections between the methods of Laplace transform, quantum canonical transform, and supersymmetry shape-invariant potentials in solving Schrodinger equations, Chinese Journal of Physics 53(4) (2015), DOI: 10.6122/CJP.20150330.

S. Viaggiu, Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform, Classical Quantum Gravity 34 (2017), 035018, DOI: 10.1088/1361-6382/aa5570.

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Published

14-11-2024
CITATION

How to Cite

Borawake, V. K., & Hiwarekar, A. P. (2024). Properties of Modified Double Laplace Transforms and Special Functions. Communications in Mathematics and Applications, 15(2), 845–854. https://doi.org/10.26713/cma.v15i2.2765

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

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