Anand International College of Engineering
Recent publications
This study focuses on a nonlinear viscoelastic wave equation involving logarithmic nonlinearity. It considers a nonlinear distributed delay influencing the boundary feedback, which is coupled with acoustic and fractional boundary conditions. Following the proof of global existence, we demonstrate the exponential growth and blow-up of solutions with positive initial energy under appropriate assumptions and for a general case of the kernel. This finding broadens and enhances earlier results. 2020 Mathematics Subject Classification. Primary: 93D20, 35L70; Secondary: 35B40, 76Exx.
This paper investigates the performance of a 32-channel Dense Wavelength Division Multiplexing Free-Space Optical (DWDM-FSO) system under various rain conditions and transmission distances ranging from 5 to 20 km. The study aims to identify optimal input power levels across different rain scenarios (-10 dBm, -5 dBm, 0 dBm, 5 dBm, and 10 dBm) to enhance the reliability and efficiency of optical communication in adverse weather. Findings indicate that for light rain conditions, input power levels of -10 dBm are suitable for distances up to 15 km. In moderate rain scenarios, -5 dBm is optimal for reliable communication up to 10 km, while higher input powers of 5 dBm are necessary to maintain performance in heavy rain conditions beyond 5 km. This study highlights the critical relationship between input power and atmospheric conditions, confirming that higher power levels can effectively mitigate the effects of rain-induced attenuation and scattering. Key parameters such as transmitter and receiver configurations, atmospheric attenuation, scattering, and turbulence were analyzed, demonstrating the importance of selecting appropriate power levels to ensure successful data transmission. Additionally, the research suggests future explorations into adaptive modulation techniques and quantum applications to further enhance system resilience and performance. The results provide valuable insights for system designers, enabling the adaptation of FSO systems to meet the challenges posed by varying environmental conditions and guiding developments in robust optical communication technologies.
In this article, an accurate optimization algorithm based on new polynomials namely generalized shifted Vieta-Fibonacci polynomials (GSVFPs) is employed to solve the nonlinear variable order time-space fractional reaction diffusion equation (NVOTSFRDE). The algorithm combines GSVFPs, new variable order fractional operational matrices in the Caputo sense, and the Lagrange multipliers to achieve the optimal solution. First, the solution of the NVOTSFRDE is approximated as a series of GSVFPs with unknown coefficients and parameters. Then, the Lagrange multipliers method is adopted so that the NVOTSFRDE can be transformed into a class of nonlinear algebraic system of equations and we solve these equations using MATLAB and MAPLE software. Solving this system and substituting the coefficients and parameters into the approximation of the guessed functions, the solution of the NVOTSFRDE is obtained. The convergence analysis of the approach are discussed. The accuracy of the algorithm is verified through error analysis and mathematical examples. The accuracy of the new method is higher than that of the exciting method. The reconstruction results demonstrate that the proposed optimization algorithm is efficient for the NVOTSFRDE, and the algorithm is also convergent.
R-method as multi criteria decision-making method was proposed to determine the ranking of alternatives and performance criteria or attributes of dental composite materials. Five alternatives (DHM0, DHM2, DHM4, DHM6, and DHM8: nomenclatures of micro-nano ceramic particulate filled dental restoration composites) and 14 attributes (performance criteria) were considered in this research. The decision-maker determined the relevance of each rank and then attributed it to the performance criterion. In a similar manner, the options were ranked in relation to each performance criterion according to the associated performance criteria. Therefore, the order of the ranks of dental composites is DHM8 (1st rank) > DHM4 (2nd rank) > DHM6 (3rd rank) > DHM0 (4th rank) > DHM2 (5th rank). The suggested technique is showed simpler and advance compared to the other generally employed decision-making techniques.
This study investigates the enhancement of dental composites using nano limestone and tricalcium phosphate fillers. Five composite formulations (TLC0-TLC4) were developed using organic polymers (Bis-GMA, TEGDMA, DMAEMA, CQ) and inorganic fillers. The methodology involved fabricating these composites and evaluating their physical and mechanical properties, including density, water absorption, solubility, polymerization shrinkage, hardness, compressive strength, and surface roughness. Results showed that density and voids increased with filler content, with TLC4 achieving the highest density at 1.39 ± 0.16 g/cm³. Water absorption and solubility increased, while polymerization shrinkage decreased to 0.66 ± 0.05% in TLC4. TLC4 demonstrated the highest hardness (72.8 ± 2.4 H.R.V.), compressive strength (248.41 ± 3.11 MPa), and surface roughness (0.62 ± 0.25 µm). Thermal analysis revealed significant weight loss and decomposition, while Fourier-transform infrared spectroscopy analysis provided detailed chemical composition insights. Wear resistance was evaluated through pin-on-disc tests and signal-to-noise ratio analysis, with FE-SEM confirming TLC4's superior performance. VIKOR analysis using the ENTROPY method ranked TLC4 as the most effective composite. This study offers valuable data for selecting and optimizing restorative dental materials.
In recent years, advancements in optimization techniques and the widespread availability of high-performance computing have made it increasingly feasible to study and develop approximation strategies for nonlinear models. This progress has empowered researchers to address more intricate and realistic challenges associated with these models. This paper introduces the application of a novel polynomial, the generalized shifted Vieta-Fibonacci polynomials (GSVFPs), in solving nonlinear variable order time fractional Burgers-Huxley equations. To mitigate storage and computational costs, new operational matrices (OMs) are devised. The proposed algorithm integrates GSVFPs, OMs, and Lagrange multipliers to achieve optimal approximations. Through convergence analysis and numerical examples, the effectiveness and accuracy of the proposed algorithm in solving these equations are demonstrated. The provided numerical illustrations further bolster this assertion.
The normalization of the generalized Struve functions Hρ,r(z)(ρ,r∈C)Hρ,r(z)(ρ,rC){\mathcal {H}}_{\rho ,r}(z) (\rho ,r\in \mathbb {C)} defined by Hρ,r(z)=∑n=0∞(-r)n4n32nρnzn,Hρ,r(z)=n=0(r)n4n(32)n(ρ)nzn,\begin{aligned} {\mathcal {H}}_{\rho ,r}(z) = \sum _{n=0}^{\infty }\frac{(-r)^n}{4^n\left( \frac{3}{2}\right) _n\left( \rho \right) _n}z^n, \end{aligned}was introduced previously and some of its geometric properties have been presented in Orhan and Yağmur (An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (NS) 63(2):229–244, 2017). In this paper, we determine conditions for Hρ,r(z)Hρ,r(z){\mathcal {H}}_{\rho ,r}(z) to be starlike and convex of different orders within the open unit disk using inequalities for the digamma function and its derivative that have been proved in Gu and Qi (J. Approx. Theory 163(9):1208–1216, 2011) as well as other preliminary lemmas in Fejér (Acta Litterarum ac Scientiarum 8:89–115, 1936) and Ozaki (Sci. Rep. Tokyo Bunrika Daigaku 2:167–188, 1935). Moreover, an efficient algorithm using MATLAB software to investigate the orders of starlikeness and convexity is presented as the first of a series. The given orders of starlikeness and convexity are then compared with some significant results in the literature to demonstrate the accuracy of our approach. Ultimately, the close-to-convexity of Hρ,r(z)Hρ,r(z){\mathcal {H}}_{\rho ,r}(z) as well as the lemniscate convexity have been evaluated using mathematical lemmas that have been given in Fejér (1936), Madaan et al. (Filomat 33(7):1937–1955, 2019) and Ozaki (1935). Further work regarding the function Hρ,r(z)Hρ,r(z){\mathcal {H}}_{\rho ,r}(z) is underway and can be presented in forthcoming articles.
Resin‐based composites, now the most prevalent material for restorative dental treatments, are available in a multitude of types. Next‐generation composites are designed to be bio interactive, solving issues such as secondary caries and mechanical failures, thus prolonging the restoration lifespan. To facilitate the discrimination of the bio interactive composite's performance and the identification of the optimal composition, we tested the VIKOR method for multi‐criteria decision‐making analysis. This study encompassed 12 performance parameters and 5 experimental dental composites. We measured density, void content, water sorption, water solubility, polymerization shrinkage, depth of cure, degree of conversion, hardness, compressive strength, and surface roughness as performance parameters, and we tested a conventional BisGMA‐TEGDMA resin blend filled with yttria‐stabilized zirconia (20 wt.%) and tricalcium phosphate. The alignment between computational methods and MATLAB‐based calculations validated the robustness of the assessment, verifying the significance of the conclusions drawn from this comprehensive analysis. Both methods (ENTROPY‐VIKOR and VIKOR‐MATLAB) ranked TZC0 as the top composite. This research provided a comprehensive understanding of the complex relationship between material composition, performance attributes, and optimization strategies in dental restorative composites, offering valuable insights for future advancements in restorative dentistry.
COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to determine the disease’s status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MATLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVID-19 affects people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.
The study introduces a fractional mathematical model in the Caputo sense for hematopoietic stem cell-based therapy, utilizing generalized Bernoulli polynomials (GBPs) and operational matrices to solve a system of nonlinear equations. The significance of the study lies in the potential therapeutic applications of hematopoietic stem cells (HSCs), particularly in the context of HIV infection treatment, and the innovative use of GBPs and Lagrange multipliers in solving the fractional hematopoietic stem cells model (FHSCM). The aim of the study is to introduce an optimization algorithm for approximating the solution of the FHSCM using GBPs and Lagrange multipliers and to provide a comprehensive exploration of the mathematical techniques employed in this context. The research methodology involves formulating operational matrices for fractional derivatives of GBPs, conducting a convergence analysis of the proposed method, and demonstrating the accuracy of the method through numerical simulations. The major conclusion is the successful introduction of GBPs in the context of the FHSCM, featuring innovative control parameters and a novel optimization technique. The study also highlights the significance of the proposed method in providing accurate solutions for the FHSCM, thus contributing to the field of mathematical modeling in biological and medical research.
The mixing of N3 and N719 metal-complex dyes was investigated in this work to determine the effects of the combination of dyes on TiO2film for application in dye-sensitized solar cells (DSSCs). The dyes were mixed in a ratio of 1:1, and their performance in the DSSCs was measured using current–voltage curves and electrochemical impedance spectroscopy (EIS). The results indicated that the efficiency of the DSSCs increased to 7% with the addition of the N719 dye to the N3 dye. The surface morphology revealed a smooth and homogeneous distribution of TiO2 nanoparticles, and the mixed dyes showed broad absorption spectra in the visible region. The EIS results indicated a low electron recombination rate and long electron lifetime for the mixed dye-sensitized solar cells. Overall, the study demonstrated the potential for using a combination of N3 and N719 dyes to improve the efficiency of DSSCs. The employment of mixed dye as a photosensitizer in DSSCs may offer a promising approach for achieving high-performance and cost-effective DSSCs.
This paper introduces and establishes new Hermite‐Hadamard type inequalities specifically tailored for m m ‐preinvex functions within the (p,q)(p,q) \left(p,q\right) ‐calculus framework. These newly developed inequalities come with accompanying left‐right estimates, which enhance their practical utility. The primary objective of this research is to investigate the properties of (p,q)(p,q) \left(p,q\right) ‐differentiable m m ‐preinvex functions and derive inequalities that extend and generalize existing results in the domain of integral inequalities. The techniques employed in this study hold broader implications, finding relevance in various fields where symmetry is paramount. The findings presented in this paper make a significant contribution to the field of analytic inequalities, offering valuable insights into the behavior and characteristics of m m ‐preinvex functions. Moreover, the established results demonstrate the wider applicability and generalization of analogous findings from prior literature. The techniques and inequalities introduced herein pave the way for further exploration and research in the realm of integral inequalities.
This study aims to propose a new optimization method based on the generalized Bessel polynomials (GBPs) as a class of basis functions for a category of nonlinear two-dimensional variable-order fractional optimal control problems (N-2D-VOFOCPs) involved in fractional-order dynamical systems and Caputo derivatives. For the optimal solution of such problems, the optimization method is developed on the basis of operational matrices (OMs) scheme of derivatives, 2D Gauss–Legendre quadrature rule, and Lagrange multiplier technique. The state and control functions are expanded in terms of the GBPs to reduce the complexity of these problems. The proposed method focuses on a system of nonlinear algebraic equations in the process of finding solution to the problems. The convergence of the method based on GBPs is proved, and the accuracy of the method is analyzed by solving several examples.
Our aim in the present paper is to present some properties involving a new class of function related to the incomplete Fox–Wright function More precisely, we derive some various properties such as differentiation formulas with respect the parameters, and fractional integration formula in terms of a class of function related to the Fox–Wright function. As applications, new summation formula containing the incomplete gamma function in terms of some special functions. In particular, new identities for some class of functions related to the Fox–Wright functions in terms of the complementary error function are established.
An enhanced transmission is presented in a multiple-input-multiple-output (MIMO) dense-wavelength division multiplexed (DWDM) free-space-optical (FSO) communication link using diversity coding techniques under the effect of turbulent weather phenomenon. The findings show good performance with an (8 channels � 2.5 Gbps data rate/channel) 20 Gbps 1500 m transmission distance. The bit-error-rate (BER), outage probability (OP), and signal-to-noise ratio (SNR) of the diversity combining techniques using maximum-ratio combining (MRC), selection combining (SC), and equal-gain combining (EGC) technique are evaluated in this work. The obtained results illustrate that Alamouti, space-time coding (STC), space-time block coding (STBC), space-time trellis code (STTC), orthogonal STBC (O-STBC), and quasi-orthogonal STBC (QO-STBC) on the minimum mean-square-error, and MRC are worth implementing on the DWDM-FSO wireless communication systems. The mitigation of atmospheric turbulence is achieved using MIMO diversity combining techniques coding. The simulation results for diversity coding techniques using QO-STBC/STTC and SC/MRC in the MIMO-DWDM FSO communication system can improve BER performance, OP, and SNR. The MRC exhibits the lowest OP and BER when compared with the SC and EGC. The numerical results demonstrate that the FSO communication link using DWDM QO-STBC/STTC improves the power penalty at both BER values under varying atmospheric turbulence conditions for ST, MT, and WT, in comparison to FSO systems without DWDM QO-STBC/STTC diversity coding techniques. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible S(t)S(t), infected I(t)I(t), treated T(t)T(t), and recovered R(t)R(t) with the susceptible category further divided into two subcategories S1(t)S1(t){S}_{1} (t) and S2(t)S2(t){S}_{2} (t). In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner.
This article reviews the theory of fairness in AI–from machine learning to federated learning, where the constraints on precision AI fairness and perspective solutions are also discussed. For a reliable and quantitative evaluation of AI fairness, many associated concepts have been proposed, formulated and classified. However, the inexplicability of machine learning systems makes it almost impossible to include all necessary details in the modelling stage to ensure fairness. The privacy worries induce the data unfairness and hence, the biases in the datasets for evaluating AI fairness are unavoidable. The imbalance between algorithms’ utility and humanization has further reinforced such worries. Even for federated learning systems, these constraints on precision AI fairness still exist. A perspective solution is to reconcile the federated learning processes and reduce biases and imbalances accordingly.
This study extended an existing semi-analytical technique, the Homotopy Perturbation Method, to the Block Homotopy Modified Perturbation Method by solving two n×n n \times n crisp triangular intuitionistic fuzzy (TIF) systems of linear equations. In the original system, the coefficient matrix is considered as real crisp, while the unknown variable vector and right hand side vector are regarded as triangular intuitionistic fuzzy numbers. The Block Homotopy Modified Perturbation Method is found to be efficient and practical to solve n×n n \times n TIF linear systems as it only requires the non-singularity of the n×n n \times n TIF linear system's coefficient matrix, whereas the point Homotopy Perturbation Method and other classical numerical iterative methods typically require non-zero diagonal entries in the coefficient matrix. A set of theorems relevant to this study are presented and demonstrated. We solve an engineering application, i.e. a current flow circuit problem that is represented in terms of a triangular intuitionistic fuzzy environment, using the suggested method. The unknown current is then obtained as a triangle intuitionistic fuzzy number. The proposed semi-analytic method is used to solve some numerical test problems in order to validate their performance and efficiency in comparison to other existing techniques. The numerical results of the example are displayed on graphs with different degrees of uncertainty. The efficiency and accuracy of the proposed method are further demonstrated by comparisons to block Jacobi, Adomain Decomposition method, Successive Over-Relaxation method and the classical Gauss-Seidel numerical method.
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84 members
Praveen Agarwal
  • Department of Physics, Chemistry, Mathematics and Humanities
Hossein Hassani
  • Department of Physics, Chemistry, Mathematics and Humanities
Anil Dhawan
  • Department of Physics, Chemistry, Mathematics and Humanities
Rahul Goyal
  • Department of Physics, Chemistry, Mathematics and Humanities
Fauzia Raza
  • Department of Mathematics
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