Muhammad Zaini Ahmad

Third-order differential subordination and superordination involving a fractional operator

Abstract The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

Periodicity computation of generalized mathematical biology problems involving delay differential equations

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann–Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.

Periodicity and positivity of a class of fractional differential equations

Fractional differential equations have been discussed in this study. We utilize the Riemann–Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

Upper and lower bounds of integral operator defined by the fractional hypergeometric function

Abstract In this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.

Solving fuzzy fractional differential equations using fuzzy Sumudu transform

In this paper, we apply fuzzy Sumudu transform (FST) for solving linear fuzzy fractional differential equations (FFDEs) involving Caputo fuzzy fractional derivative. It is followed by suggesting a new result on the property of FST for Caputo fuzzy fractional derivative. We then construct a detailed procedure on finding the solutions of linear FFDEs and finally, we demonstrate a numerical example. c ©2017 All rights reserved.

Mathematical model for adaptive evolution of populations based on a complex domain.

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function.

On some interesting properties for a new subclass of multivalent functions

In this paper, we establish a new subfamily ℘p(τ,α,β) of multivalent functions with negative coefficients that involve certain linear operator. We first investigate sharp results concerning coefficients, then obtain the distortion theorem, radius of convexity and close-to-convexity, closure theorem, neighborhood property, partial sums and integral representation.

Applications of the Fuzzy Sumudu Transform for the Solution of First Order Fuzzy Differential Equations

In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numerical example is provided to illustrate the usage of the FST.

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

This paper focuses on the application of fractional backstepping control scheme for nonlinear fractional partial differential equation (FPDE). Two types of fractional derivatives are considered in this paper, Caputo and the Grünwald-Letnikov fractional derivatives. Therefore, obtaining highly accurate approximations for this derivative is of a great importance. Here, the discretized approach for the space variable is used to transform the FPDE into a system of fractional differential equations. The convergence of the closed loop system is guaranteed in the sense of Mittag-Leffler stability. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme. c ©2017 All rights reserved.

Global and local behavior of a class of ξ(s)-QSO

A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. This paper investigates the global behavior of an operator taken from ξ(s)-QSO when the parameter a = 1 2 . Moreover, we study the local behavior of this operator at each value of a, where 0 < a < 1. c ©2017 All rights reserved.