1. ​​​​​​​​​​​​​​​​​​​​​​​​​​​​This theoretical study aims to explore the dynamics of a Casson
2. nanofluid flowing through a biological tissue under the influence of a
3. magnetic field, in the presence of an inclined circular cylindrical lymphatic
4. vessel. The governing partial differential equations and their boundary
5. conditions are transformed into a set of non-linear ordinary differential
6. equations using appropriate similarity transformations. The problem is
7. solved using the bvp4c function in MATLAB software, and the numerical
8. results are presented graphically. The research investigates and visually
9. depicts the impact of various parameters on the velocity of the nanofluid, its
10. temperature, and the concentration of nanoparticles. These parameters
11. encompass the magnetic field, porous medium, inclination angle,
12. thermophoresis, thermal Grashof number, Eckert number, mass Grashof
13. number, Casson parameter, and the curvature parameter. The study
14. concludes that an increase in the value of the Casson parameter significantly
15. elevates the NP concentration while concurrently reducing the temperature
16. of the nanofluid. We also found that there is a decreasing trend in both the
17. nanofluid temperature and the NP concentration. The two variables peak in
18. the tissue and then drop close to the lymph channel wall.

Structural, mechanical and ferromagnetic characteristics of hydrothermally synthesized Cd0.4Mn0.6XO nanocomposites were investigated. The characterization of Cd0.4Mn0.6XO was accomplished using XRD, TEM, FTIR, photoluminescence and VSM techniques. The XRD showed the formation of monoclinic Cd2Mn3O8 alongside other phases. The crystallite size has no systematic trend against the valence state of ions. The particle size has minimum value (9.75 nm) for ZnO, and maximum values of 31.39 nm and 35.61 nm were observed for Al2O3 and Fe2O3, respectively. Similarly, typical enhancements are achieved for the mechanical and ferromagnetic parameters, e.g. they are increased when ZnO is replaced by Al2O3 and significantly enhanced by Fe2O3. In contrast, they were reduced by the other X, but they are still higher than ZnO. The photoluminescence of Cd0.4Mn0.6XO shows violet, blue, green, and orange emissions. The reported results indicate a strong correlation between the mechanical and ferromagnetic properties of nanocomposites against the particle/crystallite sizes and valence state.

In this paper, we derive some classical and fractional properties of the rRs matrix function
by using the Hilfer fractional operator. The theory of special matrix functions is the theory of
those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss
hypergeometric matrix functions. We will also show the relationship with other generalized special
matrix functions in the context of the Konhauser and Laguerre matrix polynomials.

The purpose of this paper is to present some new contraction mappings via control functions. In addition, some fixed point results for Θ,α,θ,Ψ contraction, rational Θ,α,θ,Ψ contraction and almost Θ,α,θ,Ψ contraction mappings are obtained. Moreover, under contraction mappings of types (I), (II), and (III) of Θ,θ,Ψυ0, several fixed circle solutions are provided in the setting of a G-Metric space. Our results extend, unify, and generalize many previously published papers in this direction. In addition, some examples to show the reliability of our results are presented. Finally, a supporting application that discusses the possibility of a solution to a nonlinear integral equation is incorporated.

The main object of this paper is to deduce the bibasic Humbert functions Ξ1 and Ξ2
Some interesting results and elementary summations technique that was successfully employed,
q?recursion, q?derivatives relations, the q?differential recursion relations, the q?integral representations
for Ξ1 and Ξ2 are given. The summation formula derives a list of p?analogues
of transformation formulas for bibasic Humbert functions that have been studied, also some
hypergeometric functions properties of some new interesting special cases have been given.