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The behaviour of the solid tumour invasion system in the sense of Caputo fractional with time ζ and space x is analyzed by the high performance computational method: q-Homotopy Analysis Transform method (q-HATM). The existence of the solutions has been verified with the assist of fixed point theorem and derived numerical solution for different values of α,ζ,h. The novel simulation for all cases is explained through figures. We derived that the method is very efficient for analyzing the behaviour of the epidemiological system.

The motivation of this work is to analyse the nonlinear models and their complex nature with generalized tools associated with material and history-based properties. With the help of well-known and widely used numerical scheme, we study the stimulating behaviours of the financial system in this work. The impact of parameters on price index, rate of interest, investment demand, influence changes and investment cost with respect to saving amount, and the elasticity of commercial markets demand are discussed. The consequences of generalizing the model within the arbitrary order are derived. The existence of the solution for the considered system is presented. This study helps beginner researchers to investigate complex real-world problems and predict the corresponding consequences.

One of the major causes of the intermittent nature of long-term climate changes is the interaction between the surface energy balance and the mass balance of the Cryosphere. In this paper, the pre-existing surface energy balance-mass balance model of the Cryosphere is modified by incorporating the radiative forcing of CO2 to observe the effect of global warming on the nature of the previous model. The modified model is generalized using Caputo’s non-local operator. The stability of the new model is analyzed at all the equilibrium points and also it is shown that there exists a unique and bounded solution for the modified system. Using bifurcation analysis and calculating the values of Lyapunov exponents for different fractional orders of the modified system, it is found that the system exhibits chaos for certain values of the radiating forcing of CO2 To observe and visualize the changes in the nature of the new model, the system is solved using the highly efficient 7th-order Runge–Kutta method. It is observed that with the inclusion of the radiative forcing of CO2, the nature of the system changes from asymptotically stable to chaotic as we decrease the order of the system. The Poincare map shows that the modified model even has characteristics of a strange attractor which is highly chaotic. The system becomes unstable when the value of the radiative forcing of CO2 is increased. As a result, the predictive power of the surface energy balance-mass balance model of the Cryosphere decreases. In addition to providing insights into the transition from stability to chaos in the Cryosphere model due to CO2 radiative forcing, this research offers a deeper understanding of the intricate interplay between climate dynamics and complex systems behavior.

In the current studies an investigations were made to know the effect of 63 micron sized B4C particles addition on the mechanical and wear behavior of aerospace alloy Al2618 metal composites. Al2618 alloy with different weight percentages (2, 4, 6 and 8 wt. %) of 63 micron sized B4C particles reinforced composites were produced by stir cast process. These synthesized composites were tested for various mechanical properties like hardness, compression strength and tensile behavior along with density measurements. Further, microstructural characterization was carried by SEM/EDS and XRD analysis to know the micron sized particles distribution and phases. Wear behavior of Al2618 alloy with 2 to 8 wt. % of B4C composites were studied as per ASTM G99 standards with varying loads and sliding speeds. By adding 63 micron sized B4C particles hardness, compression and tensile strength of Al2618 alloy was enriched with slight decrease in elongation. Further, wear resistance of Al2618 alloy was enriched with the accumulation of B4C particles. As load and speed on the specimen increased, there was increase in wear of Al2618 alloy and its composites. Various tensile fracture surface morphology and worn surface behavior was observed by SEM analysis

The susceptible-infected-recovered (SIR) epidemic model of childhood disease is analyzed in the present framework with the help of q-homotopy analysis transform method (q-HATM). The considered model consists the system of three differential equations having fractional derivative, and the non-linear system exemplifies the evolution of childhood disease in a population and its influence on the community with susceptible, infected and recovered compartment. The projected method is a mixture of q-homotopy analysis method and Laplace transform. Two distinct explanatory cases are considered, and corresponding simulations have been demonstrated in terms of plots for different value of the order. The present investigation elucidates that the projected both derivative and technique play a vital role in the analysis and illustrate the behaviour of diverse mathematical models described with differential equations in human disease.

Technology has revolutionized the way transactions are carried out in economies across the world. India too has witnessed the introduction of numerous modes of electronic payment in the past couple of decades, including e-banking services, National Electronic Fund Transfer (NEFT), Real Time Gross Settlement (RTGS) and most recently the Unified Payments Interface (UPI). While other payment mechanisms have witnessed a gradual and consistent increase in the volume of transactions, UPI has witnessed an exponential increase in usage and is almost on par with pre-existing technologies in the volume of transactions. This study aims to employ a modified Lotka-Volterra (LV) equations (also known as the Predator-Prey Model) to study the competition among different payment mechanisms. The market share of each platform is estimated using the LV equations and combined with the estimates of the total market size obtained using the Auto-Regressive Integrated Moving Average (ARIMA) technique. The result of the model predicts that UPI will eventually overtake the conventional digital payment mechanism in terms of market share as well as volume. Thus, the model indicates a scenario where both payment mechanisms would coexist with UPI being the dominant (or more preferred) mode of payment.

In this article, we demonstrated the study of the time-fractional nonlinear Sharma-Tasso-Olever (STO) equation with different initial conditions. The novel technique, which is the mixture of the q-homotopy analysis method and the new integral transform known as Elzaki transform called, q-homotopy analysis Elzaki transform method (q-HAETM) implemented to find the adequate approximated solution of the considered problems. The wave solutions of the STO equation play a vital role in the nonlinear wave model for coastal and harbor designs. The demonstration of the considered scheme is done by carrying out some examples of time-fractional STO equations with different initial approximations. q-HAETM offers us to modulate the range of convergence of the series solution using , called the auxiliary parameter or convergence control parameter. By performing appropriate numerical simulations, the effectiveness and reliability of the considered technique are validated. The implementation of the new integral transform called the Elzaki transform along with the reliable analytical technique called the q-homotopy analysis method to examine the time-fractional nonlinear STO equation displays the novelty of the presented work. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.

The applications of hyperchaotic systems (HCSs) can be widely seen in diverse fields associated with engineering due to their complicated dynamics, randomness, and high delicacy and sensibility. In the present work, we aim to investigate a new hyper-chaotic system involving a single non-linearity under the fractional Caputo–Fabrizio (CF) derivative for the first time. In fact, there is no previous study using fractional derivatives in this system. A new mathematical system using a fractional-order operator will be designed with the novel operator. The Caputo–Fabrizio non-integer operator is aimed to be employed to capture complex nature. In order to solve the extracted dynamical system, a quadratic numerical scheme is applied. This study contains stability and convergence sections for the considered method. Moreover, numerical results of the problem under various values of fractional orders and different values of initial conditions (ICs) are provided to show the performance of the suggested scheme. Figures of solutions for each dependent variable can be observed.