Rechargeable cells can be made using two different intercalation compounds, in which the chemical potential of intercalant differs by several eV, for electrodes. We discuss factors that play a role selection appropriate lithium compounds such cells. For ease cell assembly cathode should stable air when it is fully intercalated, like . anode, intercalated Li close to metal, and then petroleum coke. Then, we show have high energy density, long cycle life, excellent high‐temperature...

This article uses fractional calculus to create novel links between the well-known Mittag-Leffler functions of one, two, three, and four parameters. Hence, this paper studies several new analytical properties using integration differentiation for function formulated by confluent hypergeometric functions. We construct a four-parameter integral expression in terms one-parameter. The explains significance applications each functions, with goal our findings make analyzing specific kinds...

The Mittag‐Leffler function (M‐LF) and confluent hypergeometric were first created in relation to the interpolation problem for exponential function. During 20th century, gamma was used introduce many formulations of these functions. Further investigation this theme led various scholars research numerous implementations applied sciences other allied disciplines. Recently, interest M‐LF has significantly developed a variety extensions generalizations forms have been posed. In research, we...

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

As of late, the study Fractional Calculus (FC) and Special Functions (SFs) has been interestingly prompted in various realms mathematics, engineering sciences. This is due to considerable demonstrated potential their applications. Among these SFs, Gamma function Mittag-Leffler functions are most renowned distinguished. Numerous authors continue this line. The current analysis attempts introduce further examine new modifications Kummer terms functions, respectively. Several attributes...

In this study, we explore the implications of a third-order differential subordination in context analytic functions associated with fractional operators. Our investigation involves consideration specific admissible classes functions. We also extend exploration to establish dual principle, resulting sandwich-type outcome. introduce these function by employing derivative operator DzαSN,Sϑz and derive conditions on normalized f that lead combination an appropriate operator.

Recently, Special Function Theory (SPFT) and Operator (OPT) have acquired a lot of concern due to their considerable applications in disciplines pure applied mathematics. The Hurwitz-Lerch Zeta type functions, as part (SPFT), are significant developing providing further new studies. In complex domain, the convolution tool is salutary technique for systematic analytical characterization geometric functions. analytic functions punctured unit disk so-called meromorphic this present analysis,...

In the z- domain, differential subordination is a complex technique of geometric function theory based on idea inequality. It has formulas in terms first, second and third derivatives. this study, we introduce some applications third-order for newly defined linear operator that includes ξ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating appropriate classes admissible functions.

Abstract According to the theory of regular geometric functions, relevance geometry analysis is a critical feature. One significant tools study operators utilize convolution product. The dynamic techniques have attracted numerous complex analyses in current research. In this effort, an attempt made by utilizing said new linear operator connecting incomplete beta function and Hurwitz–Lerch zeta certain meromorphic functions. Furthermore, we employ method based on first-order differential...

Abstract Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in open unit disk U { z : |z| < 1} for which (0) f'(0)-1=0. In this paper, we introduce study a subclass H( α, β) NH( with negative coefficients. We obtain basic results involving sufficient coefficient conditions function show these also necessary coefficients, distortion bounds, extreme points, convolution convex combinations. paper an attempt has been made to discuss some uncover...

The so-called Mittag-Leffler function (M-LF) provides solutions to the fractional differential or integral equations with numerous implementations in applied sciences and other allied disciplines. During previous century, interest M-LF has significantly developed a variety of extensions generalizations forms have been posed. Moreover, played distinguished important role Geometric Function Theory (GFT). intent current study is reveal various inclusion convolution features for specific...

Let be an infinite dimensional separable complex Hilbert space and let , where is the Banach algebra of all bounded linear operators on . In this paper we prove following results. If a operator, then 1. hypercyclic operator if only D for every hyperinvariant subspace 2. pure, countably 3. has set with dense orbit

The interest in special complex functions and their wide-ranging implementations geometric function theory (GFT) has developed tremendously. Recently, subordination been instrumentally employed for to explore properties. In this effort, by using a convolutional structure, we combine the series, logarithm, Hurwitz–Lerch zeta formulate new function, namely, logarithm-Hurwitz–Lerch (LHL-Z function). This investigation then contributes study of LHL-Z terms holomorphic functions, based on...

In this paper, we compared the Exact Bahadur Slope (EBS) and asymptotic relative efficiency of four combination methods for testing a single hypothesis against one-sided alternative in case Pareto distribution when number tests tends to infinity. These combine p-value corresponding test into one overall test. Fisher's, logistic, sum p-values, inverse normal procedures are techniques used our study. To study performance methods, derived EBS expressions limit ratios locally large values shape...

In this investigation, new integral (integrodifferential) operators in terms of the Hurwitz-Lerch Zeta Functions (HLZF) are posed. Moreover, convexity properties on generalized uniformly convex and starlike regular functions subclasses associated with these considered discussed.

In this paper, we introduce a new generalized Noor-type operator of harmonic p-valent functions associated with the Fox-Wright hypergeometric (FWGH-functions). Furthermore, consider subclass complex-valued multivalent based on operator. Several geometric properties for are also discussed.

The generalized exponential function in a complex domain is called the Mittag-Leffler (MLF). implementations of MLF are significant diverse areas science. Over past few decades, and its analysis with generalizations have become an increasingly rich research area mathematics allied fields. In geometric theory meromorphic functions, main contribution to this discipline study enrich operator on punctured domains differential inequalities, namely, subordination theory. This effort presents...

Recently, the realm related to Euler's Beta function has played a significant role in development of special theory. In this study, new extension known as with respect Mittag-Leffler-Kummer is introduced. Another formula terms Fox-Wright also presented. Numerous analytical properties function, such several functional and summation relations, Mellin transforms, integral representations, derivative formulas, are studied. Furthermore, statistical implementations distribution discussed.

In the complex field, special functions are closely related to geometric holomorphic functions. Koebe function is a notable contribution study of theory (GFT), which univalent function. This sequel introduces new class that includes more general in domain. The purpose this work present operator correlated with GFT. A generalized proposed terms convolution principle. refers generality prominent differential operator, namely Ruscheweyh operator. Theoretical investigations effort lead number...

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