Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives

We discuss existence, uniqueness and stability of solutions of the system of nonlinear fractional differential equations

     

The decay rate for a fractional differential equation

We consider the fractional differential equation

     

Positive solutions of a system of non-autonomous fractional differential equations

Existence of positive solutions for the following system of fractional differential equations:

     

Distributed order calculus and equations of ultraslow diffusion

We consider equations of the form

     

On a theorem of Levinson

Levinson investigated the number of real zeros of the real or imaginary part of

     

Tauberian theorems for double sequences that are statistically summable (C,1,1)

Let be a double sequence of real or complex numbers, and set

     

Regular approximation of singular second-order differential expressions

In this paper we construct regular real self-adjoint approximations for real self-adjoint operators associated with the differential expression

     

On a rigorous interpretation of the quantum Schrödinger-Langevin operator in bounded domains with applications

In this paper we make it mathematically rigorous the formulation of the following quantum Schrödinger-Langevin nonlinear operator for the wavefunction

     

On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials

The behaviour of real zeroes of the Hurwitz zeta-function

     

Subordination results for classes of analytic functions related to conic domains defined by a fractional operator

Let a fractional operator (n∈N₀={0,1,2,…}, 0?α<1, λ?0) be defined by

     

Estimates of majorizing sequences in the Newton-Kantorovich method: A further improvement

Let be an operator, with X and Y Banach spaces, and f^′ be Hölder continuous with exponent θ. The convergence of the sequence of Newton-Kantorovich approximations

     

Norm estimates for convolution transforms of certain classes of analytic functions

For normalized analytic functions f in the unit disk Δ, we consider the class

     

Sums of Kloosterman sums for real quadratic number fields

We estimate sums of Kloosterman sums for a real quadratic number field F of the type

     

Maximal vectors in Hilbert space and quantum entanglement

Let V be a norm-closed subset of the unit sphere of a Hilbert space H that is stable under multiplication by scalars of absolute value 1. A maximal vector (for V) is a unit vector ξ∈H whose distance to V is maximum

     

The porous medium equation in a two-component domain

We consider a system of two porous medium equations defined on two different components of the real line, which are connected by the nonlinear contact condition

     

Adomian decomposition: a tool for solving a system of fractional differential equations

Adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations. Convergence of the method has been discussed with some illustrative examples. In particular, for the initial value problem: