Solution of Abel-type integral equation involving the Appell hypergeometric function

The present paper gives a formal solution of a certain Abel-type integral equation involving the Appell hypergeometric function in the kernel. The integral equation and its solution give rise to new forms of generalized fractional calculus operators (viz. the generalized fractional integrals and generalized fractional derivatives). These and their various consequences are also mentioned. The concluding remarks briefly point out possibilities of further work concerning the operators studied in this paper.