### 0n the Domain Of Attraction of Stable and of Extreme Value Distributions

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2000 Mathematics Subject Classification: 26A33, 33C60, 44A20In this survey we present a brief history and the basic ideas of the generalized fractional calculus (GFC). The notion “generalized operator of fractional integration” appeared in the papers of the jubilarian Prof. S.L. Kalla in the years 1969-1979 when he suggested the general form of these operators and studied examples of them whose kernels were special functions as the Gauss and generalized hypergeometric functions, including arbitrary...

In this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.

Mathematics Subject Classification: 35CXX, 26A33, 35S10The well known Duhamel principle allows to reduce the Cauchy problem for linear inhomogeneous partial differential equations to the Cauchy problem for corresponding homogeneous equations. In the paper one of the possible generalizations of the classical Duhamel principle to the time-fractional pseudo-differential equations is established.* This work partially supported by NIH grant P20 GMO67594.

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution which shows how the...

In this paper we investigate the global existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of implicit hyperbolic fractional order differential equations by using a nonlinear alternative of Leray-Schauder type for contraction maps on Fréchet spaces.

This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.

In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.