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1.
A. Guezane-Lakoud 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2692-2700
Using Banach contraction principle and Leray-Schauder nonlinear alternative we establish sufficient conditions for the existence and uniqueness of solutions for boundary value problems for fractional differential equations with fractional integral condition, involving the Caputo fractional derivative. Some examples are given to illustrate our results. 相似文献
2.
We invert the Weyl integral transform by means of a generalized continuous wavelet transform on the half line associated with the Bessel operatorL
, >–1/2. Next, we use the connection between radial classical wavelets onR
n
and generalized wavelets associated with the Bessel operatorL(
n–2)/2 to derive new inversion formulas for the Radon transform onR
n
,n2. 相似文献
3.
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin–Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox–Wright functions. A series expansion is also provided in order to point out the distribution of time-scales related to the distribution of the fractional orders. The results of the time fractional diffusion equation of a single order are also recalled and then re-obtained from the general theory. 相似文献
4.
5.
A formal definition of fractional integrals in the complex matrix variate case is given here. This definition will encompass all the various fractional integral operators introduced by various authors in the real scalar and matrix cases. The new definition is introduced in terms of M-convolutions of products and ratios of matrices in the complex domain. Their connections to statistical distribution theory, Mellin convolutions, M-transforms and Mellin transform are pointed out. Some basic properties are given and a pathway extension of the new definition is also given. The pathway extension will provide a switching mechanism to move among three different families of functions. 相似文献
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7.
Suppose 1≤p,q≤∞ and α > (1/p−1/q)+. Then we investigate compactness properties of the integral operator when regarded as operator from Lp[0,1] into Lq[0,1]. We prove that its Kolmogorov numbers tend to zero faster than exp(−cαn1/2). This extends former results of Laptev in the case p=q=2 and of the authors for p=2 and q=∞. As application we investigate compactness properties of related integral operators as, for example, of the difference
between the fractional integration operators of Riemann–Liouville and Weyl type. It is shown that both types of fractional
integration operators possess the same degree of compactness. In some cases this allows to determine the strong asymptotic
behavior of the Kolmogorov numbers of Riemann–Liouville operators.
In memoria of Eduard (University of the West Indies) who passed away in October 2004. 相似文献
8.
Alan Macdonald 《Advances in Applied Clifford Algebras》1998,8(1):5-16
Using recent advances in integration theory, we give a proof of the fundamental theorem of geometric calculus. We assume only
that the tangential derivative ∇
V
F exists and is Lebesgue integrable. We also give sufficient conditions that ∇
V
F exists. 相似文献
9.
We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. 相似文献
10.
11.
This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations. 相似文献
12.
The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type. 相似文献
13.
George A. Anastassiou 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5440-5445
Here we establish mixed Caputo fractional ‖.‖p, Landau type inequalities, p∈(1,∞]. We give applications on R. 相似文献
14.
In this paper, we study fractional differential inclusions with Dirichlet boundary conditions. We prove the existence of a solution under both convexity and nonconvexity conditions on the multi-valued right-hand side. The proofs rely on nonlinear alternative Leray–Schauder type, Bressan–Colombo selection theorem and Covitz and Nadler’s fixed point theorem for multi-valued contractions. The compactness of the set solutions and relaxation results is also established. In the last section we consider the fractional boundary value problem with infinite delay. 相似文献
15.
Aurelian Cernea 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):204-208
Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov’s theorem for a fractional differential inclusion. 相似文献
16.
The paper presents a simple new approach to the problem of computing Fourier transforms of SO(d)-finite measures on the unit sphere in the euclidean space. Representing such measures as restrictions of homogeneous polynomials we use the canonical decomposition of homogeneous polynomials together with the plane wave expansion to derive a formula expressing such transforms under two forms, one of which was established previously by F. J. Gonzalez Vieli. We showthat equivalence of these two forms is related to a certain multi-step recurrence relation for Bessel functions, which encompasses several classical identities satisfied by Bessel functions. We show it leads further to a certain periodicity relation for the Hankel transform, related to the Bochner- Coifman periodicity relation for the Fourier transform. The purported novelty of this approach rests on the systematic use of the detailed form of the canonical decomposition of homogeneous polynomials, which replaces the more traditional approach based on integral identities related to the Funk-Hecke theorem. In fact, in the companion paper the present authors were able to deduce this way a fairly general expansion theorem for zonal functions, which includes the plane wave expansion used here as a special case.Received: 7 May 2004; revised: 11 October 2004 相似文献
17.
Alan D. Sokal 《Expositiones Mathematicae》2010,28(2):179-185
We obtain a characterization of generalized Stieltjes functions of any order λ>0 in terms of inequalities for their derivatives on (0,∞). When λ=1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938. 相似文献
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19.
Xinwei Su 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(8):2844-2852
In this paper, by means of Darbo’s fixed point theorem, we establish the existence result of solutions to a boundary value problem of fractional differential equation on the half-line in a Banach space. An example illustrating our main result is given. 相似文献
20.
In this paper, we shall discuss the properties of the well-known Mittag-Leffler function, and consider the existence and uniqueness of the solution of the periodic boundary value problem for a fractional differential equation involving a Riemann-Liouville fractional derivative by using the monotone iterative method. 相似文献