The Mittag-Leffler function and confluent hypergeometric functions were created to approximate interpolation in exponential functions. researchers noted that Prabhakar’s integral transformation, which involves extended multi-parameter functions, may be used create explore different fractional calculus models. This four-parameter is further illustrated graphs using MATLAB. With classical (Riemann–Liouville) integrals, the research shows a set of formulations for these differintegral...

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...

Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how glucose excess, estrogen and anxiety work together to affect speed at which breast cells multiply immune system’s response model is necessary conceive ways stop spread cancer. This paper proposes mathematical investigate impact psychological panic, excess on interaction immunity. The proposed precisely described. focus model’s dynamic analysis identify potential equilibrium locations....

Abstract Optimal control theory is an extension of the calculus variations. It a mathematical optimization method for deriving strategies dynamic system. In this paper, system differential equations which we aim to utilize TikTok, one most attractive internet platforms. TikTok has garnered immense popularity, surpassing other social media However, its addictive nature raised concerns about mental health, including depression, eating disorders, anxiety, self-obsession, and narcissistic...

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...

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...

The results obtained by the authors in present article refer to quantum calculus applications regarding theories of strong differential subordination and superordination. q-analogue multiplier transformation is extended, order be applied on specific classes functions involved superordination theories. Using this extended transformation, a new class analytic normalized introduced investigated. convexity set belonging proven symmetry properties derive from characteristic class. Additionally,...

By using a linear operator with Hurwitz-Lerch-Zeta function, which is defined here by means of the Hadamard product (or convolution), author investigates interesting properties certain subclasses meromorphically univalent functions in punctured unit disk <svg style="vertical-align:-0.23206pt;width:20.700001px;" id="M1" height="14.0375" version="1.1" viewBox="0 0 20.700001 14.0375" width="20.700001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g...

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.

By using a linear operator associated with the λ-generalized Hurwitz–Lerch zeta function, which is defined here by means of Hadamard product (or convolution), authors introduce and investigate various properties certain subclasses meromorphically univalent functions in punctured unit disk. Some closely related (known or new) corollaries consequences main results presented this paper are also considered.

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 this article, we apply the Daftardar-Gejji and Jafari method (DJM) to solve multispecies Lotka–Volterra equation. A comparison between DJM, differential transformation (DTM), variational iteration (VIM), Adomian decomposition (ADM) shows that DJM is a reliable powerful for solving nonlinear equations. The efficiency applicability of are confirmed by considering some examples. proposed procedure provides better results in existing methods.

&lt;abstract&gt; &lt;p&gt;The quadratic Riccati equations are first-order nonlinear differential with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their solutions. This paper provided the approximate solution of equation via cubic b-spline method. The convergence analysis method is discussed. efficiency applicability proposed approach verified through three test problems. obtained results good...

In this paper, we propose the new iterative method (NIM) for solving generalized Burgers–Huxley equation. NIM provides an approximate solution without need discretization and is based on a set of equations. We compared with other established methods, such as Variational Iteration Method (VIM), Adomian Decomposition (ADM), exact solution, found that it efficient easy to use. has advantage quick convergence, implementation, handling wide range initial conditions. The comparison present...

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this we define family of analytic non-Bazilevič functions, denoted as Tq,τ+1,uμ(ϑ,λ,M,N). Furthermore, investigate differential subordination properties univalent functions using q-calculus, includes best dominance, subordination, and sandwich-type properties. Our results are proven specialized techniques in theory.

This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville’s fractional integral and Caputo derivative. approach eliminates need assumptions about parameter magnitudes, offering a significant advantage. We validate our using time-fractional Cahn–Hilliard, Burgers–Poisson, Benjamin–Bona–Mahony–Burger equations. Comparative testing shows that outperforms new iterative, homotopy...

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...