Mathematics Subject Classification: 26A33, 33C20.
The paper is devoted to the study of the fractional calculus of the generalized Wright function
pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series
pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered.
* The present investigation...

The paper is devoted to the study of the Cauchy problem for a nonlinear
differential equation of complex order with the Caputo fractional derivative.
The equivalence of this problem and a nonlinear Volterra integral equation
in the space of continuously differentiable functions is established. On the
basis of this result, the existence and uniqueness of the solution of the
considered Cauchy problem is proved. The approximate-iterative method
by Dzjadyk is used to obtain the approximate solution...

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99
The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in...

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.
The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the...

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50,
33C60, 26A09
Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product...

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33
The paper is devoted to the study of the Cauchy-type problem for the
differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15
The paper is devoted to the study of the function Zνρ(x) defined for
positive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0
for ρ ≤ 0, [...]
Such a function was earlier investigated for ρ > 0. Using the Mellin transform
of Zνρ(x), we establish its representations in terms of the H-function
and extend this function from positive x > 0 to complex z. The results
obtained, being different for ρ >...

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