On a \(q\)-analogue of the Elzaki transform called mangontarum \(q\)-transform (Q2321512)

Summary: 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.