Search

In this research, we combine ideas from geometric function theory and fuzzy set theory. We define a new operator Dτ−λLα,ζm:A→A of analytic functions in the open unit disc Δ with the help of the Riemann–Liouville fractional integral operator, the linear combination of the Noor integral operator, and the generalized Sălăgean differential operator. Further, we use this newly defined operator Dτ−λLα,ζm together with a fuzzy set, and we next define a new class of analytic functions denoted by Rϝζ(m,α,δ). Several innovative results are found using the concept of fuzzy differential subordination for the functions belonging to this newly defined class, Rϝζ(m,α,δ). The study includes examples that demonstrate the application of the fundamental theorems and corollaries.

In this paper, we find values of depth, Stanley depth, and projective dimension of the quotient rings of the edge ideals associated with r-fold bristled graphs of ladder graphs, circular ladder graphs, some king’s graphs, and circular king’s graphs.

In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order α, strong starlikeness, and some inclusion results. We also study radii problems for various classes of analytic functions. Furthermore, we investigate some coefficient-related problems which include the sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three.

This paper introduces a new fractional operator by using the concepts of fractional q-calculus and q-Mittag-Leffler functions. With this fractional operator, Janowski functions are generalized and studied regarding their certain geometric characteristics. It also establishes the solution of the complex Briot–Bouquet differential equation by using the newly defined operator.

This study deals with analytic functions with bounded turnings, defined in the disk Od=z:z<1. These functions are subordinated by sigmoid function 21+e−z and their class is denoted by BTSg. Sharp coefficient inequalities, including the third Hankel determinant for class BTSg, were investigated here. The same was also included for the logarithmic coefficients related to functions of the class BTSg.

In this paper, we apply the pseudospectral method based on the Chebyshev cardinal function to solve the parabolic partial integro-differential equations (PIDEs). Since these equations play a key role in mathematics, physics, and engineering, finding an appropriate solution is important. We use an efficient method to solve PIDEs, especially for the integral part. Unlike when using Chebyshev functions, when using Chebyshev cardinal functions it is no longer necessary to integrate to find expansion coefficients of a given function. This reduces the computation. The convergence analysis is investigated and some numerical examples guarantee our theoretical results. We compare the presented method with others. The results confirm the efficiency and accuracy of the method.

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.