On Another Type of Transform Called Rangaig Transform

Norodin A. Rangaig^1, , 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

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

Abstract

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 log_ex=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.

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

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