<p>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.</p>

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On Generalized Quaternion Integral Transform and its Applications

  • Pinakadhar Baliarsingh,
  • Swaraj Sahoo

摘要

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.