Based upon a new general vector-valued vector product, generalized complex numbers with respect to certain positively homogeneous functionals including norms and antinorms are introduced and a vector-valued Euler type formula for them is derived usin...
In this paper, we investigate closed-form meromorphic solutions of the fifth-order Sawada-Kotera (fSK) equation and (3+1)-dimensional generalized shallow water (gSW) equation. The study of high-order and high-dimensional differential equations is piv...
In this paper, we introduce the concept of generalized Fourier series, generated by the p-trigonometric functions, namely cosp and sinp, recently introduced related to the generalized complex numbers systems. The aim of this study is to represent a p...
A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential ope...
In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some appli...
In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic f...
We propose the notion of
This paper intends to define degenerate q-Hermite polynomials, namely degenerate q-Hermite polynomials by means of generating function. Some significant properties of degenerate q-Hermite polynomials such as recurrence relations, explicit identities...
This paper introduces fractional operators in the complex domain as generalizations for the Srivastava–Owa operators. Some properties for the above operators are also provided. We discuss the convexity and starlikeness of the generalized Libera...
(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional...
The existence or nonexistence of a complex structure on a differential manifold is a central problem in differential geometry. In particular, this problem on
The paper expands the finite difference method to the complex plane, and thus obtains an improvement in the resolution of differential equations with an increase in numerical precision and a generalization in the mathematical modeling of problems. Th...
Three-dimensional models, reconstructed from real-life objects, are extensively used in virtual and mixed reality technologies. In this paper we propose an approach to 3D model reconstruction via inverse procedural modeling and describe two variants...
The generalized exponential function in a complex domain is called the Mittag-Leffler function (MLF). The implementations of MLF are significant in diverse areas of science. Over the past few decades, MLF and its analysis with generalizations have be...
Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are i...
Non-zero differential initial values hinder the application of fractional operator theory in practical systems. This paper proposes a differential initial values zeroing method, decomposing functions with non-zero differential initial values into a c...
In this work, we introduce a generalization of the differential polynomial neural network utilizing fractional calculus. Fractional calculus is taken in the sense of the Caputo differential operator. It approximates a multi-parametric function with p...
In this paper, we propose new complex and real pair-wise detection for conventional differential space–time modulations based on quasi-orthogonal design with four transmit antennas for general QAM. Since the new complex and real pair-wise detections...
A self-organizing joint system classical oscillator–random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness generated...
Degenerate versions of polynomial sequences have been recently studied to obtain useful properties such as symmetric identities by introducing degenerate exponential-type generating functions. As part of our continued work in degenerate versions of g...
In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more comp...
We define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investi...
First trimester placental development comprises some of the most critical yet understudied events that impact fetal development. Improper placentation leads to a host of health issues that not only impact the fetal period but also influence offspring...
Telomeres are specialized nucleoprotein complexes, localized at the physical ends of chromosomes, that contribute to the maintenance of genome stability. One of the features of chronic myeloid leukemia (CML) cells is a reduction in telomere length wh...
Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed differential equati...
The design of differential evolution (DE) operators has long been a key topic in the research of metaheuristic algorithms. This paper systematically reviews the functional differences between mechanism improvements and operator improvements in terms...
A new linear integro-differential equation is considered on a closed curve located on the complex plane. The integrals in the equation are understood in the sense of a finite part, according to Hadamard. The order of the equation can be higher than o...
Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gr...
Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory. The fractio...
An important problem in complex analysis is to determine properties of the image of an analytic function p defined on the unit disc U from an inclusion or containment relation involving several of the derivatives of p. Results dealing with differenti...
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain...
In this study, we investigate coupled real and complex dispersionless equations for curve families, even if they have singular points. Even though the connections with the differential equations and regular curves were considered in various ways in t...
By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral ope...
Concentrated growth factors (CGF) is the newest generation platelet concentrate product, which has been reported to promote the proliferation and differentiation of human dental pulp cells (hDPCs). However, the effect of liquid phase of CGF (LPCGF) h...
Recently, a lot of attention has been paid to the field of research connected with the wireless sensor network and industrial internet of things. The solutions found by theorists are next used in practice in such area as smart industries, smart devic...
Epidermal differentiation is a complex process and its regulation may involve epigenetic factors. Analysis of DNA methylation in 20 selected regions within the epidermal differentiation complex (EDC) gene cluster by targeted next-generation sequencin...
A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involv...
The functional complexity of higher organisms is not easily accounted for by the size of their genomes. Rather, complexity appears to be generated by transcriptional, translational, and post-translational mechanisms and tissue organization that produ...
In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications...
This study presents a tripartite analytical framework for the (1+1)-dimensional nonlinear Klein–Fock–Gordon equation, a key model for spinless particles in relativistic quantum mechanics. The investigation begins with a Painlevé an...
Acetylation of histones is a key epigenetic modification involved in transcriptional regulation. The addition of acetyl groups to histone tails generally reduces histone-DNA interactions in the nucleosome leading to increased accessibility for transc...
This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. This work aims to present new fuzzy differential subordinations for which the fuzzy best dominant and fuzzy bes...
We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local Kähler identities to t...
Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function...
This work examines a new subclass of generalized bi-subordinate functions of complex order
The loss mechanism of transonic axial compressors is a long-standing problem that involves almost all types of entropy generation in fluid flows, such as skin friction, shock waves, shear flows, corner separation, and tip vortices. Primarily, sources...
Epidermal stem cells sustain the adult skin for a lifetime through self-renewal and the production of committed progenitors. These stem cells generate progeny that will undergo terminal differentiation leading to the development of a protective epide...
In this paper, symmetry analysis is extended to study nonlocal differential equations. In particular, two integrable nonlocal equations are investigated, the nonlocal nonlinear Schrödinger equation and the nonlocal modified Korteweg–de Vri...
Initially, the concept of the complexity reduction approach was applied to solve symmetry algebraic systems that were generated from the discretization of the partial differential equations. Consequently, in this paper, the effectiveness of a complex...
This paper introduces an enhanced Iterative Finite Difference (IFD) method for efficiently solving strongly nonlinear, time-dependent problems. Extending the original IFD framework for nonlinear ordinary differential equations, we generalize the appr...
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