On a q -Analogue of the Elzaki Transform Called Mangontarum q -Transform

الملخص EN

Two q -analogues of the Elzaki transform, called Mangontarum q -transforms, are introduced in this paper.

Properties such as the transforms of q -trigonometric functions, transform of q -derivatives, duality relation, convolution identity, q -derivative of transforms, and transform of the Heaviside function are derived and presented.

Moreover, we will consider applications of the Mangontarum q -transform of the first kind to some ordinary q -differential equations with initial values.