Certain classes of ordinary and partial differential equations solvable by means of fractional calculus

摘要

Recently, many workers demonstrated the usefulness of fractional calculus in the derivation of particular solutions of a considerably large number of linear ordinary and partial differential equations of the second and higher orders. The main object of the present paper is to show how readily some recent contributions on this subject by S.-T. Tu, K. Nishimoto, S.-J. Jaw, and S.-D. Lin [Hiroshima Math. J. 23 (1993) 63–77] (and by other workers) can be obtained by suitably applying some general theorems on particular solutions of a certain family of linear ordinary and partial fractional differintegral equations.