An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.

Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯), f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

Entropic pressure controls the oligomerization of the Vibrio cholerae ParD2 antitoxin

ParD2 is the antitoxin component of the parDE2 toxin–antitoxin module from Vibrio cholerae and consists of an ordered DNA-binding domain followed by an intrinsically disordered ParE-neutralizing domain. In the absence of the C-terminal intrinsically disordered protein (IDP) domain, V. cholerae ParD2 (VcParD2) crystallizes as a doughnut-shaped hexadecamer formed by the association of eight dimers. This assembly is stabilized via hydrogen bonds and salt bridges rather than by hydrophobic contacts. In solution, oligomerization of the full-length protein is restricted to a stable, open decamer or dodecamer, which is likely to be a consequence of entropic pressure from the IDP tails. The relative positioning of successive VcParD2 dimers mimics the arrangement of Streptococcus agalactiae CopG dimers on their operator and allows an extended operator to wrap around the VcParD2 oligomer.

Certain fundamental properties of generalized natural transform in generalized spaces

This paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

Entropic pressure controls oligomerization of Vibrio cholerae ParD2 antitoxin

ParD2 is the antitoxin component of the parDE2 toxin-antitoxin module from Vibrio cholerae and consists of an ordered DNA binding domain followed by an intrinsically disordered ParE-neutralizing domain. In absence of the C-terminal IDP domain, VcParD2 crystallizes as a doughnut-shaped hexadecamer formed by the association of eight dimers. This assembly is stabilized via hydrogen bonds and salt bridges rather than hydrophobic contacts. In solution, oligomerization of the full-length protein is restricted to a stable, open 10-mer or 12-mer, likely as a consequence of entropic pressure from the IDP tails. The relative positioning of successive VcParD2 dimers mimics the arrangement of Streptococcus agalactiae CopG dimers on their operator and allows for an extended operator to wrap around the VcParD2 oligomer.

Fractional heat equation optimized by a chaotic function

In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.

Extending operator method to local fractional evolution equations in fluids

This paper is aimed to solve non-linear local fractional evolution equations in fluids by extending the operator method proposed by Zenonas Navickas. Firstly, we give the definitions of the generalized operator of local fractional differentiation and the multiplicative local fractional operator. Secondly, some properties of the defined operators are proved. Thirdly, a solution in the form of operator representation of a local fractional ordinary differential equation is obtained by the extended operator method. Finally, with the help of the obtained solution in the form of operator representation and the fractional complex transform, the local fractional Kadomtsev-Petviashvili (KP) equation and the fractional Benjamin-Bona-Mahoney (BBM) equation are solved. It is shown that the extended operator method can be used for solving some other non-linear local fractional evolution equations in fluids.

Finite continuum quasi distributions from lattice QCD

We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via perturbation theory.