We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the me...

We deal with applications of the transform T? we introduced in our paper On a generalized function-to-sequence transform, Appl. Anal. Disc. Math. Vol. 14 No 2 (2020) 300-316. Taking different sequences {?n}n?N0 linked to linear difference operator D? gives rise family transforms that enables mapping differential equation and its solutions solutions. It can map one as well.

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the Beta and obtain certain integral differential representation of them. Further, we present some formulas Riemann-–Liouville fractional integration differentiation operators. Also, derive various transforms, including Euler transform, Laplace Whittakar transform K-transform. The operator images are expressed in terms...

We study asymptotics of orthogonal polynomial measures of the form |HN |2dγ where HN are real or complex Hermite polynomials with respect to the Gaussian measure γ. By means of differential equations on Laplace transforms, interpolation between the (real) arcsine law and the (complex) uniform distribution on the circle is emphasized. Suitable averages by an independent uniform law give rise to ...

We present a model for genetic regulatory networks with time delays, which is described by functional differential equations or delay differential equations (DDE), provide necessary and sufficient conditions for simplifying the genetic network model, and further analyze nonlinear properties of the model in terms of local stability and bifurcation. The proposed model transforms the original inte...

a cochlear implant is an implanted electronic device used to provide a sensation of hearing to a person who is hard of hearing. the cochlear implant is often referred to as a bionic ear. this paper presents an undecimated wavelet‑based speech coding strategy for cochlear implants, which gives a novel speech processor. the undecimated wavelet packet transform (uwpt) is computed like the wavelet ...

A lot of problems the physical world can be modeled by non-linear ODE with their initial and boundary conditions. Especially higher order differential equations play a vital role in this process. The method for solution its effectiveness are as important modelling. In paper, on basis reproducing kernel theory, functions have been obtained solving some equations. Additionally, each problem homog...

a dynamic two dimensional problem of thermoelasticity with double porous structure has been considered to investigate the disturbance due to normal force and thermal source. laplace and fourier transform technique is applied to the governing equations to solve the problem. the transformed components of stress and temperature distribution are obtained .the resulting expressions are obtained in t...

The main goal of this paper is to describe the new version extended Bessel–Maitland function and discuss its special cases. Then, using aforementioned as their kernels, we develop generalized fractional integral differential operators. convergence boundedness newly operators compare them with existing such Saigo Riemann–Liouville are explored. transforms defined in terms Fox–Wright presented. A...