Search Results (33)

In the recent past, a number of research articles have explored the stability, existence, and uniqueness of the solutions and controllability of dynamical systems with a fractional order (FO). Nevertheless, aside from the controllability and other dynamical aspects, very little attention has been given to the observability of FO dynamical systems. This paper formulates a novel type of FO delay system of the Pantograph type in the Caputo sense and explores its controllability and observability results. This research endeavor begins with the conversion of the proposed dynamical system into a fixed-point problem by utilizing Laplace transforms, the convolution of Laplace functions, and the Mittag–Leffler function (MLF). We then set out Gramian matrices for both the controllability and observability of the linear parts of our proposed dynamical system and prove that both the Gramian matrices are invertible, thus confirming the controllability and observability in a given domain. Considering the controllability and observability results of the linear part along with some other assumptions, we investigate the controllability and observability results related to the nonlinear system. The Banach contraction result, the fixed-point result of Schaefer, the MLF, and the Caputo FO derivative are used as the main tools for establishing these results. To establish the authenticity of the established results, we add two examples at the end of the manuscript. Full article

Human dermal fibroblasts play an important role in skin homeostasis by producing and degrading extracellular matrix components. They have more replicative senescence when exposed to environmental and oxidative insults, resulting in human skin aging. However, this phenomenon can be mitigated by antioxidant phytochemicals. The aim of the present study was to investigate the potential of nuciferine (an alkaloid from Nelumbo nucifera leaf) in preventing stress-induced fibroblast senescence by using a hydrogen-peroxide (H₂O₂)-induced senescence model. We found that H₂O₂ treatment resulted in a significant increase in senescence-associated β-galactosidase (SA-β-gal)-positive cells. Nuciferine-treated cells, however, showed a reduction in senescent phenotype. Furthermore, we observed the key molecular markers including the senescence-associated secretory phenotype (SASP) and cell cycle regulators. The mRNA levels of CXCL1, CXCL2, IL-6, and IL-8 (pro-inflammatory cytokines) reduced significantly in nuciferine-treated cells. The extracellular IL-6 and IL-8 levels were also decreased in treated cells, whereas the key cell cycle regulators (p16 and p21) were markedly affected by nuciferine at the highest concentration. The results of the present study clearly show that the preventive activity of nuciferine against H₂O₂-induced senescence in dermal fibroblasts is fundamental and promising for further applications in anti-aging product research and development. Full article

The Darcy ternary hybrid nanofluid flow comprising titanium dioxide (TiO₂), cobalt ferrite (CoFe₂O₄) and magnesium oxide (MgO) nanoparticles (NPs) through wedge, cone, and plate surfaces is reported in the present study. TiO₂, CoFe₂O₄, and MgO NPs were dispersed in water to synthesize a trihybrid nanofluid. For this purpose, a mathematical model was calculated to augment the energy transport rate and efficiency for variety of commercial and medical functions. The consequences of heat source/sink, activation energy, and the magnetic field are also analyzed. Such problems mostly occur in symmetrical phenomena and are applicable to engineering, physics, and applied mathematics. The phenomena were formulated in the form of a nonlinear system of PDEs, which are simplified to the system of dimensionless ODEs through similarity replacement (obtained from symmetry analysis). The obtained set of differential equations is resolved through a parametric continuation approach (PCM). Graphical depictions are used to evaluate and address the impact of significant factors on energy, mass, and flow exchange rates. The velocity and energy propagation rates over a cone surface were greater than those of a wedge and plate versus the variation of Grashof number, porosity effect, and heat source, while the mass transfer ratio under the impact of a chemical reaction and activation energy over a wedge surface was higher than that of a plate. Full article

Studies associated with ethylene glycol (EG) have great significance in various engineering sectors because EG is more useful as a cooling agent in various engines. Furthermore, fluid inspection using two distinct nanoparticles has applications in mechanical systems, electronic devices, medical apparatus, and the diagnosis and treatment of disease. Therefore, present comminution explored the entropy production in magnetized hybrid nanomaterials flowing via Darcy–Forchheimer space with varying permeability. Hybrid nano liquid is synthesized by adding cobalt ferrite and gold nanoparticles to ethylene glycol and water. Effects of thermal radiation, Joule heating, heat sources, and an exponential heat source are considered in the energy expression. The assumed problem is modeled in the form of nonlinear PDEs. Such types of problems have mostly occurred in symmetrical phenomena and are applicable in engineering, physics, and applied mathematics. The obtained system is converted to ODEs using suitable substitution transformations. Resultant ODEs are numerically computed with the help of the NDSolve technique using Mathematica software. Their outcomes are displayed through figures and tables. Obtained results reveal that variable permeability and curvature parameters improve the velocity profile, while an exponential heat source (EHS) enhances the thermal effect. It is also observed that entropy optimization improves with the increment in magnetic parameter. Full article

In this study, we investigated a radiative chemically reactive Casson fluid above a cone, plate, and wedge with gyrotactic microorganisms subjected to the Cattaneo–Christov heat flux model. Newton’s method and the Runge–Kutta methods were employed to solve the physical problem, and a graphical representation of the numerous impacts of non-dimensional parameters on temperature, velocity, and concentration was created. In addition, we also compared recently published solutions with our current solution, which showed good agreement. From this investigation, we concluded that the motile organisms’ momentum, temperature, and concentration density were non-uniform in nature. Here, for engineering importance, we also present the mass transfer and thermal transfer rate over the cone, wedge, and plate cases in a tabular form. We concluded that the mass and heat transfer rate was larger over the cone when compared to the same case over a plate or wedge. The results also highlighted that the local Nusselt and Sherwood numbers and the mass density of the microorganisms depreciated as the Casson fluid parameter decreased. In summary, we concluded that the gyrotactic microorganisms played a role in enhancing the local Sherwood number. Full article

In this study, the dispersal caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using the nonlinear longitudinal wave equation (LWE), a mathematical physics problem. Using the generalized exp-function method, we investigate the families of solitary wave solutions of one-dimensional nonlinear LWE. Using the computer program Wolfram Mathematica 10, these new exact and solitary wave solutions of the LWE are derived as trigonometric function, periodic solitary wave, rational function, hyperbolic function, bright and dark solitons solutions, sinh, cosh, and sech² function solutions of the LWE. These solutions represent the electrostatic potential and pressure for LWE as well as the graphical representation of electrostatic potential and pressure. Full article

This study investigates the fractional-order Swift–Hohenberg equations using the natural decomposition method with non-singular kernel derivatives. The fractional derivative in the sense of Caputo–Fabrizio is considered. The Adomian decomposition technique (ADT) is a great deal to the overall natural transformation to create closed-form results of the given models. This technique provides a closed-form result for the suggested models. In addition, this technique is attractive, simple, and preferred over other techniques. The graphs of the solution in fractional and integer-order show that the achieved solutions are very close to the actual result of the examples. It is also investigated that the result of fractional-order models converges to the integer-order model’s solution. Furthermore, the proposed method validity is examined using numerical examples. The obtained results for the given problems fully support the theory of the proposed method. The present method is a straightforward and accurate analytical method to analyze other fractional-order partial differential equations, such as many evolution equations that govern the dynamics of nonlinear waves in plasma physics. Full article

In this article, we study the novel features of morphological effects for hybrid nanofluid flow subject to expanding/contracting geometry. The nanoparticles are incorporated due to their extraordinary thermal conductivity and innovative work for hybrid nanofluids, which are assembled of aluminum oxides, Al₂O₃ metallic oxides, and metallic copper Cu. Cu nanoparticles demonstrate very strong catalytic activity, while Al₂O₃ nanoparticles perform well as an electrical insulator. The governing partial differential equations of the elaborated model are transformed into a system of nonlinear ordinary differential equations with the use of similarity variables, and these equations are numerically solved through a shooting technique based on the Runge–Kutta method. We develop a hybrid correlation for thermophysical properties based on a single-phase approach. A favorable comparison between shape and size factors for metallic and metallic-oxide nanoparticles is discussed via tables and figures. Moreover, the effect of embedding flow factors on concentration, velocity, and temperature is shaped in line with parametric studies, such as the permeable Reynolds number, nanoparticle volume fractions, and expansion/contraction parameters. The fluid velocity, temperature, and concentration are demonstrated in the presence of hybrid nanoparticles and are discussed in detail, while physical parameters such as the shear stress, flow of heat, and mass transfer at the lower and upper disks are demonstrated in a table. The hybrid nanoparticles show significant results as compared to the nanofluids. If we increase the nanoparticle volume fraction, this increases the thermal performance for an injection/suction case as well. The above collaborative research provides a strong foundation in the field of biomedical equipment and for the development of nanotechnology-oriented computers. Full article

The current work investigated the mass and heat transfer of the MHD hybrid nanofluid flow subject to the impact of activation energy and cluster interfacial nanolayer. The heat transport processes related to the interfacial nanolayer between nanoparticles and base fluids enhanced the base fluid’s thermal conductivity. The tiny particles of $F{e}_3{O}_4$ and $PPy$ were considered due to the extraordinary thermal conductivity which is of remarkable significance in nanotechnology, electronic devices, and modern shaped heat exchangers. Using the similarity approach, the governing higher-order nonlinear coupled partial differential equation was reduced to a system of ordinary differential equations (ODEs). Fe₃O₄–PPy hybrid nanoparticles have a considerable influence on thermal performance, and when compared to non-interfacial nanolayer thermal conductivity, the interfacial nanolayer thermal conductivity model produced substantial findings. The increase in nanolayer thickness from level 1 to level 5 had a significant influence on thermal performance improvement. Further, the heat and mass transfer rate was enhanced with higher input values of interfacial nanolayer thickness. Full article

The energy and mass transition through Newtonian hybrid nanofluid flow comprised of copper Cu and aluminum oxide (Al₂O₃) nanoparticles (nps) over an extended surface has been reported. The thermal and velocity slip conditions are also considered. Such a type of physical problems mostly occurs in symmetrical phenomena and are applicable in physics, engineering, applied mathematics, and computer science. For desired outputs, the fluid flow has been studied under the consequences of the Darcy effect, thermophoresis diffusion and Brownian motion, heat absorption, viscous dissipation, and thermal radiation. An inclined magnetic field is applied to fluid flow to regulate the flow stream. Hybrid nanofluid is created by the dispensation of Cu and Al₂O₃ nps in the base fluid (water). For this purpose, the flow dynamics have been designed as a system of nonlinear PDEs, which are simplified to a system of dimensionless ODEs through resemblance substitution. The parametric continuation method is used to resolve the obtained set of dimensionless differential equations. It has been noticed that the consequences of heat absorption and thermal radiation boost the energy transmission rate; however, the effect of suction constraint and Darcy–Forchhemier significantly diminished the heat transference rate of hybrid nanofluids. Furthermore, the dispersion of Cu and Al₂O₃ nps in the base fluid remarkably magnifies the velocity and energy transmission rate. Full article

This numerical investigation effectively establishes a unique computing exploration for steady magnetohydrodynamic convective streams of tangent hyperbolic nanofluid traveling across a nonlinearly elongating elastic surface with a variable thickness. In addition, the importance of an externally imposed magnetic field of tangent hyperbolic nanofluid is comprehensively analyzed by considering the substantial impact of thermal conductivity and thermal radiation consequences. The governing PDEs (partial differential equations) are transmuted into a nonlinear differential structure of coupled ODEs (ordinary differential equations) using a series of variable similarity transformations. Furthermore, these generated ODEs (ordinary differential equations) are numerically set using a novel revolutionary Runge-Kutta algorithm with a shooting approach constructed in a MATLAB script. In this regard, extensive comparison studies are carried out to validate the acquired numerical results. The interactions between the associated profiles and the relevant parameters are rationally explored and shown using graphs and tabular forms. The velocity distribution declined with improving Weissengberg number $We$ and power-law index m, while the reverse performance can be observed for temperature. As enhancement in Brownian motion, Thermophoretic and radiation parameters significantly rise in temperature distribution. The use of many different technological and industrial systems, including nano-bioconvective systems, nano-droplet evaporation, nano-ink jet printing, and microbial fuel cells, would benefit this research study. Full article

This work combines a ZZ transformation with the Adomian decomposition method to solve the fractional-order Fokker-Planck equations. The fractional derivative is represented in the Atangana-Baleanu derivative. It is looked at with graphs that show that the accurate and estimated results are close to each other, indicating that the method works. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series type result that quickly converges to actual answers. The acquired outcomes suggest that the novel analytical solution method is simple to use and very successful at assessing complicated equations that occur in related research and engineering fields. Full article

In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining the approximate analytical solution of the fractional Kuramoto–Sivashinsky equation (FKS). The proposed method gives a series form solution which converges quickly towards the exact solution. To show the accuracy of the proposed method, we examine three different cases. We presented proposed method results by means of graphs and tables to ensure proposed method validity. Further, the behavior of the achieved results for the fractional order is also presented. The results we obtain by implementing the proposed method shows that our technique is extremely efficient and simple to investigate the behaviour of nonlinear models found in science and technology. Full article

This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique are applied to solve the suggested problems. The proposed method has an advantage over existing approaches because it does not require additional materials or computations. Four problems are used to test the authenticity of the proposed method. Using the suggested method, the solution proves to be more accurate. The proposed method can be implemented to solve many nonlinear fractional order problems because it has a straightforward implementation. Full article

The lid-driven top wall’s influence combined with the side walls’ waviness map induce the mixed convection heat transfer, flow behavior, and entropy generation of a hybrid nanofluid (Fe₃O₄–MWCNT/water), a process analyzed through the present study. The working fluid occupies a permeable cubic chamber and is subjected to a magnetic field. The governing equations are solved by employing the GFEM method. The results show that the magnetic force significantly affects the working fluid’s thermal and flow behavior, where the magnetic force’s perpendicular direction remarkably improves the thermal distribution at Re = 500. Also, increasing Ha and decreasing Re drops both the irreversibility and the heat transfer rate. In addition, the highest undulation number on the wavy-sided walls gives the best heat transfer rate and the highest irreversibility. Full article