The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying 181 –
200 of
363
We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative over I,...
Mathematics Subject Classification: 26A33, 47A60, 30C15.In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.
Using variational methods, we investigate the solutions of a class of fractional Schrödinger equations with perturbation. The existence criteria of infinitely many solutions are established by symmetric mountain pass theorem, which extend the results in the related study. An example is also given to illustrate our results.
We study the local well-posed integrated Cauchy problem
, v(0) = 0, t ∈ [0,κ),
with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.
MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA connection between fractional calculus and statistical distribution
theory has been established by the authors recently. Some extensions of
the results to matrix-variate functions were also considered. In the present
article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional...
MSC 2010: 26A33We study mixed Riemann-Liouville integrals of functions of two variables in Hölder spaces of different orders in each variables. We consider Hölder spaces defined both by first order differences in each variable and also by the mixed second order difference, the main interest being in the evaluation of the latter for the mixed fractional integral in both the cases where the density of the integral belongs to the Hölder class defined by usual or mixed differences. The obtained results...
If is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form
u (Pf) Cv (f)
are established for a general class of functions . Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.
Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation
models governed by distributed fractional order differential equations
(DODEs) and multi-term fractional order differential equations are constructed.
The construction is based on the discretization leading to a generalized
difference scheme (containing a finite number of terms in the time
step and infinite number of terms in the space step) of the Cauchy problem
for...
The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).
Currently displaying 181 –
200 of
363