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

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.