Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution....

Let G be a graph of order n, and let k ≥ 2 and m ≥ 0 be two integers. Let h : E(G) → [0, 1] be a function. If ∑ e∋x h(e) = k holds for each x ∈ V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(...

Because of the nonlocal and nonsingular properties fractional derivatives, they are more suitable for modelling complex processes than integer derivatives. In this paper, we use a factor to investigate Hamilton’s canonical equations Poisson theorem mechanical systems. Firstly, derivative integral with presented, multivariable differential calculus is given. Secondly, obtained under new definiti...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

Studies were performed in anesthetized dogs (n = 5) to determine the effects of synthetic atrial natriuretic factor on renal function and renin release. Intrarenal infusion of synthetic atrial natriuretic factor (ANF) (0.3 microgram X kg-1 X min-1) resulted in a transient increase in renal blood flow (126 +/- 8 to 148 +/- 11 ml/min). The duration of this transient vasodilation was 3.1 +/- 0.4 m...

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending the tractability of many problems in dat...