This paper introduces a generalized quaternion integral transform, which generalizes most of the integral transforms in quaternion space. In this work, we discuss some properties of the transform along with its direct applications to reduce and solve quaternion differential equations. A new area of research is explored, which involves quaternions of fractional calculus. In this context, some well-known fractional differential equations have been solved in quaternion space using the defined generalized quaternion integral transform. 

This paper deals with the generalized conformable fractional derivative and certain interesting properties which are not compatible with Riemann-Liouville and Caputo fractional derivatives. The newly defined derivative is more efficient than other conformable fractional derivatives and the nonlocal fractional derivatives from a time perspective. To justify the claim, we provide some direct applications, such as population growth, Newton’s body cooling, heat equation and susceptible-infected-removed models. Solutions obtained from models and comparison with respective previous data are demonstrated with the help of graphs or stems.