The aim of this work is to demonstrate various an interesting recursion formulas, dierential
and integral operators, integration formulas, and innite summation for each of Horn's hypergeometric
functions H1, H2, H3, H4, H5, H6 and H7 by the contiguous relations of Horn's hypergeometric series.
Some interesting dierent cases of our main consequences are additionally constructed.

Inspired by the recent work Sahin and Agha gave recursion formulas for G1 and G2 Horn
hypergeometric functions (Sahin and Agha in Miskolc Math Notes 16(2):1153–1162, 2015).
The object of work is to establish several new recursion relations, relevant differential recursion
formulas, new integral operators, infinite summations and interesting results for Horn’s
hypergeometric functions G1, G2 and G3.

Agarwal et al. (2021) established the extension of several fundamental contiguous relations for GB. Our aim in this work is to investigate several properties of differentiation formulas, differential equations, recursion relations, differential recursion relations, confluence formulas, series representations, integration formulas, and infinite summations for Horn’s hypergeometric function GB of three variables. Some well-known particular cases have additionally been given.

The main aim of this work is to derive the q-recurrence relations, q-partial derivative relations
and summation formula of bibasic Humbert hypergeometric function 1 on two independent
bases q and q1 of two variables and some developments formulae, believed to be new, by using
the conception of q-calculus.

In this paper, we derive some classical and fractional properties of the ??? 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 main aim of present work is to investigate the dynamics of the chaotic nonlinear distributed order Lü model (DOLM). The distributed order (DO) derivative is used for describing the viscoelasticity of various technical models and materials. The modified spectral numerical method is used to evaluate the numerical solutions for DOLM. Using nonlinear feedback control and the Lyapunov direct approach, the adaptive synchronization of two chaotic distributed order models (DOMs) is presented. We state a theorem to drive analytical controllers which are used to achieve our synchronization. The DOLM is introduced as an example of DOMs to verify the validity of our analytical results. Numerical computations are displayed to show the agreement between both analytical and numerical results. The DOMs appear in many applications in engineering and physics, e.g., image encryption and electronic circuits (ECs). Based on our proposed synchronization, the encryption and decryption of color images are studied. Information entropy, visual analysis and histograms are calculated, together with the experimental results of image encryption and decryption. We design the EC of the DOLM using the Multisim circuit simulator for the first time to our knowledge. Using electronic circuit simulation, we achieved the same results for the numerical treatment of our synchronization. Other ECs can be similarly designed for other DOMs.

In this work, we propose three chaotic (or hyperchaotic) models. These models are real or complex with one stable equilibrium point (hidden attractor). Based on a modified Sprott E model, three versions were introduced: the complex integer order, the real fractional order, and the complex fractional order. The basic properties of these models have been studied. We discover that the complex integer-order version has chaotic and hyperchaotic multi-scroll hidden attractors (MSHAs) by computing Lyapunov exponents (LEs). By making a small change to a model parameter, different MSHA values can be produced for this version. The dynamics of the real fractional version are investigated through a bifurcation diagram and LEs. It has chaotic hidden attractors for various fractional-order q values. Through varying the model parameters of the complex fractional-order (FO) version, different numbers of chaotic MSHAs can be generated. Due to the complex dynamic behaviors of the MSHAs, these models may have several applications in physics, secure communications, social relations and image encryption. Anew kind of combination synchronization (CS) between one integer-order drive model and two FO response models with different dimensions is proposed. The tracking control method is used to investigate a scheme for this type of synchronization. As an example, we used our three models to test the validity of this scheme, and an agreement between the analytical and numerical results was found.

We report here the effect of annealing temperature T_ann (200–600 °C) on the structural, mechanical, and magnetic properties of Cd_0.40M_0.60ZnO₂ (M = Mn, Ni) nanocomposites. The increase in T_ann correlates with a significant change in unit cell volume (V), porosity (PS) crystallite size (D_hkl), particle size (r), Debye temperature (θ_D) and elastic modulus(Y). The values of V, r, θ_D and Y are higher for the Mn-series than Ni. While the values of PS and D_hkl are higher for Mn than Ni at T_ann ≤ 300 °C, and the reverse is true at T_ann ≥ 400 °C. The average particle size is 10.6 ± 2.4 nm for Mn-series, but it is decreased to 7.5 ± 4.0 nm for Ni-series, indicating quantum-dot size. Surprisingly, both series exhibit ferromagnetic behavior as T_ann increases to 600 °C, but the magnetization parameters for the Mn series are higher than those for Ni. Furthermore, the anisotropy field (H_a) is about 350 times higher than the corrective field (H_c), indicating hard magnetic materials. The switching field distribution (SFD) is increased by annealing, but it is higher for Ni-series than Mn. The considered nanocomposites would be useful for altering plastic deformation and spintronic devices.

Schistosomiasis is the second most prevailing parasitic disease worldwide. Although praziquantel is considered an effective drug in the treatment against schistosomiasis to some extent, there is an emerging drug resistance that widely recorded. Therefore, there is an urgent need to develop effective and safe anti-schistosomal drugs. In this study, Cornulaca monacantha (C. monacantha), a sub-saharan plant, was extracted using aqueous ethanol and characterized by High-Performance Liquid Chromatography (HPLC). Major constituents of the extract are belonging to flavonoids, tannins and phenolic glycosides. Worms’ viability and surface morphology of Schistosoma mansoni (S. mansoni) adult worms treated with the extract were assessed using in vitro viability assay, Scanning Electron Microscopy (SEM), and histological examination. The extract (80–350 μg/ml) reduced viability percentage of worms by 40–60% and caused degeneration of both oral and ventral suckers, tegumental, sub-tegumental and muscular damage. Molecular docking approach was utilized to assess the binding affinities of the extracted compounds with S. mansoni alpha-carbonic anhydrase (SmCA), an essential tegument protein. Pharmacokinetic analysis using SwissADME showed that 7 compounds have high drug similarity. This study confirms the in vitro schistomicidal activity of C. monacantha extract against S. mansoni adult worms and suggests potential SmCA inhibition.