In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

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 this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, establish bounds initial coefficients υ2, υ3, and υ4 Taylor–Maclaurin series that Fekete–Szegö functional associated with classes, give many consequences our findings.

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

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

The paper introduces a new family of analytic bi-univalent functions that are injective and possess inverses, by employing q-analogue the derivative operator. Moreover, article establishes upper bounds Taylor–Maclaurin coefficients these functions, which can aid in approximating accuracy approximations using finite number terms. obtained Faber polynomial expansions. These apply to both initial ...

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

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,...

in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...