ANALYTICAL APPROACH TO A CLASS OF BAGLEY-TORVIK EQUATIONS

Abstract

Multi-term fractional differential equations have been studied because of their applications in modelling, and solved using miscellaneous mathematical methods. We present explicit analytical solutions for several families of generalized multidimensional Bagley-Torvik equations with permutable matrices and two various fractional orders which are satisfying alpha is an element of (1, 2], beta is an element of (0, 1] and alpha is an element of (1, 2], alpha is an element of (1, 2], both homogeneous and inhomogeneous cases. The results are obtained by means of Mittag-Leffler type matrix functions with double infinite series. In addition, we acquire general solutions of the Bagley-Torvik scalar equations with 1/2-order and 3/2-order derivatives. At the end, we present different examples to verify the efficiency our main results.