Related papers: Leinartas's partial fraction decomposition
In this paper, we propose a solution of fractional logistic equation by using properties of Mittag-Leffler function.
This paper introduces a very fast method for the computation of the resolvent of fractional powers of operators. The analysis is kept in the continuous setting of (potentially unbounded) self adjoint positive operators in Hilbert spaces.…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…
We provide new formulas for the coefficients in the partial fraction decomposition of the restricted partition generating function. These techniques allow us to partially resolve a recent conjecture of Sills and Zeilberger. We also describe…
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary…
We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally with basic known properties of Lerch zeta, and use the…
The recent theory of fractional $h$-difference equations introduced in [N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems, Signal Process. 91 (2011), no. 3, 513--524], is enriched with useful…
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted…