Explicit solutions to hyper-Bessel integral equations of second kind

AbstractIn earlier papers, the authors have used the transmutation method to find solutions to Volterra integral or differ-integral equations of second kind, involving Erdélyi-Kober fractional integration operators (see [1,2]), as well as to dual integral equations and some Bessel-type differential equations (see [3,4]). Here we consider the so-called hyper-Bessel integral equations whose kernel-function is a rather general special function (a Meijer's G-function). Such an equation can be written also in a form involving a product of arbitrary number of Erdélyi-Kober integrals. By means of a Poisson-type transmutation, we reduce its solution to the well-known solution of a simpler Volterra equation involving Riemann-Liouville integration only. In the general case, the solution is found as a series of integrals of G-functions, easily reducible to series of G-functions. For particular nonhomogeneous (right-hand side) parts, this solution reduces to some known special functions. The main techniques are based on the generalized fractional calculus

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

MSC 2010: 35R11, 42A38, 26A33, 33E12The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of the Fox H-functions. The results derived are of general nature and include already known results as particular cases

An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.Comment: 7 pages, LaTe

Fractional Noether's theorem in the Riesz-Caputo sense

We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.Comment: Accepted (25/Jan/2010) for publication in Applied Mathematics and Computatio

Dynamic Load Distribution in MIST

Abstract: This paper presents an algorithm for scheduling parallel applications in large-scale, multiuser, heterogeneous distributed systems. The approach is primarily targeted at systems that harvest idle cycles in general-purpose workstation networks, but is also applicable to clustered computer systems and massively parallel processors. The algorithm handles unequal processor capacities, multiple architecture types and dynamic variations in the number of processes and available processors. Scheduling decisions are driven by the desire to minimize turnaround time while maintaining fairness among competing applications. For efficiency, the virtual processors (VPs) of each application are gang scheduled on some subset of the available physical processors

The pressure broadening of spectral lines A unified theory for the Van Der Waals interaction

SIGLEAvailable from British Library Document Supply Centre- DSC:D70074/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Some results on generalized elliptic-type integrals

Abstract In this paper we study a fam r TI ly of integra Is of the form where O 6 k < 1, Re(p) > -and m is a nonnegative integer. Such integrals occur in radiation field problems. We obtain a series expansion and establish its relationship with Gauss' hypergeometric function. Asymptotlc expansions val id in the neighbourhood of k2=l are given.0ne of these formulas has been obtained by the use of an Abel ian theorem. Some recurrence relations are established. Results obtained earlier by Epstein and Hubbell, and Weiss follow as particular cases of our formulae given here. Some numerical values of ~~ ( k , m ) for selected values of the parameter are tabulated, using different formulae

A generalization of elliptic-type integrals

The method o f steepest descent i s employed t o o b t a i n r e l a t i o n s between KV(k,m), sU(k,v) and incornplete gamma f u n c t i o n s . W e t a b u l a t e these e l -1 t p t i c -t y p e i n t e g r a l s by u s i n g s u i t a b l e formulae. Some k n o w n r e s u l t s f o l l o w as p a r t i c u l a r cases o f o u r formulae e s t a b l i s h e d here. I n a r e c e n t paperl, t h e a u t h o r s have s t u d i e d a fami l y o f i n t eg r a l s where O $ k < 1, ~e ( u ) > -and m i s a non-negative i n t e g e r . For m = O and = j , a p o s i t i v e i n t e g e r where O < k < 1, a fami 1 y o f i n t e g r a l s considered by E p s t e i n and Hubbel 12.such i n t e g r a l s a r e found i n t h e a p p l i c a t i o n o f t h e Legendre polynomial expans i o n method 3 t o c e r t a i n problems i n v o l v i n g computation o f t h e r a d i a t i o

Dynamic Load Distribution in MIST

This paper presents an algorithm for scheduling parallel applications in large-scale, multiuser, heterogeneous distributed systems. The approach is primarily targeted at systems that harvest idle cycles in general-purpose workstation networks, but is also applicable to clustered computer systems and massively parallel processors. The algorithm handles unequal processor capacities, multiple architecture types and dynamic variations in the number of processes and available processors. Scheduling decisions are driven by the desire to minimize turnaround time while maintaining fairness among competing applications. For efficiency, the virtual processors (VPs) of each application are gang scheduled on some subset of the available physical processors

A certain family of infinite series associated with Digamma functions

AbstractThe sums of several interesting infinite series were recently expressed in terms of the Psi (or Digamma) functions. The object of this paper is to present a systematic account of these (and of numerous similar or more general) series whose sums can be found in the literature in various equivalent forms. Some relevant unifications and further generalizations are also indicated