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In this article, we first consider the fractional q-differential operator and the λ,q-fractional differintegral operator Dqλ:A→A. Using the λ,q-fractional differintegral operator, we define two new subclasses of analytic functions: the subclass S*q,β,λ of starlike functions of order β and the class CΣλ,qα of bi-close-to-convex functions of order β. We explore the results on coefficient inequality and Fekete–Szegö problems for functions belonging to the class S*q,β,λ. Using the Faber polynomial technique, we derive upper bounds for the nth coefficient of functions in the class of bi-close-to-convex functions of order β. We also investigate the erratic behavior of the initial coefficients in the class CΣλ,qα of bi-close-to-convex functions. Furthermore, we address some known problems to demonstrate the connection between our new work and existing research.

In the field of nano-composites, hybrid nano-fluids have noteworthy applications in aerospace, energy materials, thermal sensors, antifouling, etc. because of their ability to produce higher thermal conductivity than conventional nanofluids. Different combinations of nanocomposites have been found in the literature to develop the suitable hybrid-mixture, but no study has been found yet about the combined influence of ceria and zinc-oxide nanocomposites in the host liquid. In this article, unsteady 3 D transport of water driven hybrid nano-fluid with the consequences of brick shaped nanocomposites (ceria; and zinc oxide; ) has deliberated with the thermal link of heat source/sink. Variable thermal conditions have been supplied at the surface with the effect of a magnetic environment. Similarity relations have been used to articulate the transport equations into solvable forms and then solved numerically via Keller-Box method. Nusselt number and skin-friction coefficients have also plotted with the wide ranges of involved parameters. Thermal setup has also briefly been discussed with the non-uniformity of surface temperature. Rate of heat transfer has significantly improved with the amounts of ceria (1 wt% to 10 wt%) and zinc-oxide (1 wt% to 10 wt%) nanocomposites. The Nusselt number is reported in the range of 4.0 to 4.8 with the increasing amount of from −0.6 to −0.2, whereas it is reported in the range of 3.1 to 3.9 with the varying amount of from 0.2 to 0.6. Rate of heat transfer is observed higher for zinc-oxide nanoparticles as compared to ceria nanoparticles.

In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BSα,λm,t:An→An in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BSα,λm,t. By considering linear transformations of the operator BSα,λm,t, we define a new fuzzy class of analytic functions in U which we denote by Tϝλ,t(m,α,δ). Several innovative results are found using the concept of fuzzy differential subordination and the operator BSα,λm,t for the function f in the class Tϝλ,t(m,α,δ). In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies.

The recent progress in nanotechnology provides the concept of hybrid-class nano-fluids having advanced thermal features comparing to regular nanofluids. The idea of a hybrid nanofluid has motivated many researchers because of its convincible performance in thermal systems. The novel theme of the present effort is to scrutinize the consequences of convective heat transfer in bidirectional water driven hybridclass nanofluid involving blade shaped cadmium telluride CdTe and graphite C nanoparticles with electromagnetohydrodynamics (EMHD) process. The transport equations representing the aforementioned topic are firstly nondimensionalized by using scaling-group transformation and then tackled by the Keller-box method, numerically. The significant results for pertinent parameters have been simulated and presented graphically as well as in tabular forms. Coefficients of drag forces are diminished with the more loadings of cadmium telluride and graphite nanoparticles and opposite results are noticed in the case of the Nusselt number. Heat transport has been improved significantly with more loadings of nanoparticles from 1 wt% to 10 wt%. A comparison benchmark for a limited version of the investigation is made with the previously published data.

In the current work, by using the familiar q-calculus, first, we study certain generalized conic-type regions. We then introduce and study a subclass of the multivalent q-starlike functions that map the open unit disk into the generalized conic domain. Next, we study potentially effective outcomes such as sufficient restrictions and the Fekete–Szegö type inequalities. We attain lower bounds for the ratio of a good few functions related to this lately established class and sequences of the partial sums. Furthermore, we acquire a number of attributes of the corresponding class of q-starlike functions having negative Taylor–Maclaurin coefficients, including distortion theorems. Moreover, various important corollaries are carried out. The new explorations appear to be in line with a good few prior commissions and the current area of our recent investigation.

Background Regardless of the advancements in ophthalmology, rhegmatogenous retinal detachment (RRD) remains a substantial issue for physicians. The present study assessed the incidence of RRD among our population. Methodology A cross-sectional study was performed at the Layton Rehmatullah Benevolent Trust (LRBT) between June 2020 and May 2021. All the patients of RRD, irrespective of gender, within the age bracket of 20 years or more and diagnosed by a consultant ophthalmologist were included in the research study. Patients with serous retinal or tractional detachment and RRD with vitreous leakage were excluded from the study. A slit lamp and dilated fundus examination was performed preoperatively to assess the type of retinal detachment and associated factors as mentioned above. All data were collected on predesigned pro forma. Results About 25,000 individuals were presented to the outpatient department during the study period. Out of these, 100 patients were diagnosed with RRD. The incidence rate of the RRD in our center was 0.4%. There were a majority of the males. The mean age of patients did not vary significantly with respect to gender (p < 0.797). The most common type of RD was the total RD with a frequency of 53 cases followed by inferior RD with 19 cases. The majority of those with total RRD were males, i.e., 37%; however, the difference was statistically insignificant (p = 0.476). The study revealed that most of the RRD was diagnosed in patients < 45 years of age; however, the difference was not statistically significant (p < 0.227). Conclusion The present study highlighted the incidence of RRD and explored the sociodemographic and other clinical features in the Pakistani population. However, it is possible that the RRD condition is still under-diagnosed in our hospital settings. Further exploration is warranted to study comprehensively the risk factors associated with RRD., Competing Interests: The authors have declared that no competing interests exist., (Copyright © 2022, Iqbal et al.)