Analytic solutions of fractional integro-differential equations of Volterra type with variable coefficients

作者：Tomovski Zivorad^*; Garra Roberto

来源：Fractional Calculus and Applied Analysis, 2014, 17(1): 38-60.

DOI：10.2478/s13540-014-0154-8

• fractional integro-differential equation
• Laguerre derivatives
• Mittag-Leffler function
• multinomial Mittag-Leffler function

In this paper we study explicit solutions of fractional integro-differential equations with variable coefficients involving Prabhakar-type operators. Analytic solutions to equations involving Prabhakar operators and Laguerre derivatives are obtained by means of operational methods.
Cauchy type problems for fractional integro-differential equations of Volterra type with generalized Riemann-Liouville derivative operator, which contain generalized Mittag-Leffler function in the kernel are also considered. Using the Laplace transform method, explicit solutions of the fractional integro-differential equations of Volterra type with variable coefficients, proposed by Srivastava and Tomovski in [28] are established in terms of the multinomial Wright function.

• 出版日期2014-3