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Some Volterra-type fractional integro-differential equations with a multivariable confluent hypergeometric function as their kernel. (English) Zbl 1086.45002
The solution is obtained for an integro-differential equation of Volterra type, of the second kind, with fractional integral operators, and involving the Lauricella function \(\Phi_2(n)\) in the kernel. The Laplace transformation provides the method of solution. The resolvent kernel, and other functions which appear as a result of the initial conditions, are given in terms of functions represented by infinite series of \(\Phi_2^{(n)}\) functions. The Kummer function \(_1F_1\) provides an interesting special case which is treated as a corollary.

45J05 Integro-ordinary differential equations
33C65 Appell, Horn and Lauricella functions
26A33 Fractional derivatives and integrals
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