The present paper deals with the solution of Abel integral equation involving Fox- H function. The method is based on approximations of fractional integrals and Caputo derivatives due to Jahanshahi et al. The approximation formula of Abel integral equation using numerical trapezoidal rule is also obtained. The paper is also illustrating the effectiveness of proposed approach in form of many particular examples. The results are mostly derived in a closed form in terms of the H-function, suitable for numerical computation. On account of general nature of H-function a number of results involving special functions can be obtained merely by specializing the parameters.

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Abel Integral Equations Fox H-function Riemann–liouville Fractional Derivatives Caputo Fractional Derivatives.