The paper proposes a new approach to compute the impulse response of fractional order linear time invariant systems. By applying a general approach to decompose a Laplace transform into a Laurent like series, we obtain a power series that generalizes the Taylor and MacLaurin series. The algorithm is applied to the computation of the impulse response of causal linear fractional order systems. In...

In the current work, we introduce a special family of function analytic and m-fold symmetric bi-univalent functions obtain estimates Taylor–Maclaurin coefficients |dm+1| |d2m+1| for in family. For ? real number, Fekete–Szegö functional |d2m+1??dm+12| is also estimated. We indicate several cases defined connections to existing results are discussed.

Motivated by q-calculus, we define a new family of Σ, which is the bi-univalent analytic functions in open unit disc U that related to Einstein function E(z). We establish estimates for first two Taylor–Maclaurin coefficients |a2|, |a3|, and Fekete–Szegö inequality a3−μa22 belong these families.

The purpose of this article is to introduce a new subclass analytic and bi-univalent functions, in associated with sigmoid function investigate the upper bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Further we obtain Fekete-Szego inequalities class sigma. We also give several illustrative examples functionclass which here.

In this paper, we introduce and investigate new subclasses (Yamakawa-type bi-starlike functions another class of Lashin, both mentioned in the reference list) bi-univalent defined open unit disk, which are associated with Gegenbauer polynomials satisfy subordination conditions. Furthermore, find estimates for Taylor–Maclaurin coefficients |a2| |a3| these subclasses. Several known or consequence...

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc this work. provide estimates for first two Taylor–Maclaurin series coefficients these functions. Furthermore, we define Salagean differential operator and discuss various applications our main findings using it. A few well-known corollaries are studied order to show connection between recent earlier

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients,...

The aim of the present article is to introduce and investigate a new family LΣ(δ,η,θ,t;h) normalized holomorphic bi-univalent functions that involve Sakaguchi-type Bazilevič θ-pseudo-starlike associated with Laguerre polynomials. We obtain estimates on initial Taylor–Maclaurin coefficients Fekete–Szegö problem for in this family. Properties symmetry can be studied newly functions.

In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of newly defined and class analytic bi-univalent functions associated q-derivative operator. Furthermore, find initial Taylor–Maclaurin coefficients for these function classes functions. also show that bounds are sharp. The sharp second Hankel determinant is given class.

In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function σm m-fold symmetric bi-univalent functions defined in open unit disc D and obtain estimates first two Taylor–Maclaurin coefficients for family. Further, Fekete–Szegö functional is also estimated. The results presented paper not only generalize improve some recent works, but give new as cases.