International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: Editor-in-chief: Mahammad Nurmammadov
Open Access
Journal Browser
International Journal of Partial Differential Equations and Applications. 2017, 5(1), 42-48
DOI: 10.12691/ijpdea-5-1-6
Open AccessArticle

On Another Type of Transform Called Rangaig Transform

Norodin A. Rangaig1, , Norhamida D. Minor1, Grema Fe I. Pe~nonal1, Jae Lord Dexter C. Filipinas1 and Vernie C. Convicto1

1Department of Physics, Mindanao State University-Main Campus, Marawi City 9700, Philippines

Pub. Date: December 19, 2017

Cite this paper:
Norodin A. Rangaig, Norhamida D. Minor, Grema Fe I. Pe~nonal, Jae Lord Dexter C. Filipinas and Vernie C. Convicto. On Another Type of Transform Called Rangaig Transform. International Journal of Partial Differential Equations and Applications. 2017; 5(1):42-48. doi: 10.12691/ijpdea-5-1-6


A new Integral Transform was introduced in this paper. Fundamental properties of this transform were derived and presented such as the convolution identity, and step Heaviside function. It is proven and tested to solve some basic linear-differential equations and had succesfully solved the Abel's Generalized equation and derived the Volterra Integral Equation of the second kind by means of Initial Value Problem. The Natural Logarithm (e.g logex=lnx) has been established and defined by means of modifying the Euler Definite Integral based on the Rangaig's fomulation. Hence, this transform may solve some different kind of integral and differential equations and it competes with other known transforms like Laplace, Sumudu and Elzaki Transform. Keywords: Rangaig Transform, Integral Transform, linear ordinary differential function, Integro-differential equation, Convolution Theorem.

rangaig transform integral transform linear ordinary dierential function integro-dierential equation convolution theorem

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  E. D. Rainvill and P. E. Bedient, Elementary Differential Equations, 6th ed., Macmillian Publishing Co., Inc., New York, pp. 170-232, 1981.
[2]  L. Debnath, D. Bhatta, Integral Transform and thier Application, 2nd Edition; Chapman and Hall/CRC, 2006.
[3]  G. B Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed., Elsevier Inc., pp. 965-071, 2005.
[4]  G. K. Watugala, Sumudu Transform- a new Integral Transform to Solve differential Equation and Controlling Enginnering, Math. Eng'g Induct., vol. 6, no.1, pp. 319-329, 1998.
[5]  T. M. Elzaki, The New Integral Transform Elzaki transform, Global Journal of Pure and AppliedMathematic, vol. 7, no. 1, pp. 57-64, 2011.
[6]  Zhang J., A Sumudu Based Algoritm for Solving Differential equations, Comp. Sci. J. Moldova, vol. 3, no. 15, pp. 303-313, 2009.
[7]  T. Elzaki, S. Elzaki, and E. Elnour, On some applications of new integral transform 'Elzaki Transform', The Global Journal of Mathematical Sciences: Theory and Practical, vol. 4, no. 1, pp. 15-23, 2012.
[8]  S. Weera Koon, Application of Sumudu Transform to Partial Differential Equation. Int. J. Math. Educ. Sc. Tech., vol. 25, no. 2, pp. 277-283, 1994.
[9]  T. M. Elzaki and S. M. Ezaki, On the connections between Laplace and ELzaki transforms, Adv. Theo. and Appl. Math., vol.67 no. 6, pp. 1-10. 2011.
[10]  T. M. Elzaki, S. M. Ezaki and E. M.A. Hilal, ELzaki and Sumudu transform for solving some differential equations Global Journal of Pure and Applied Mathematic, vol. 4, no. 8, pp. 167-173, 2012.
[11]  M. R. Spiegel, S. Lipschutz, J. Liu, Mathematical Handbook and Formulas and Tables, Third Edition, McGraw-Hill Comp. 2009.
[12]  S. T. Thornton ST, J. B. Marion JB, Classical Dynamics of Particles and Systems, Fifth Edition, Academic Press, 2004.
[13]  G. Arfken, Mathematical Methods for Physicist, 4th edition; Academic Press, New York, (1985).