Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (p, q)-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced. Further, a new generalized form of the fractional kinetic equation involving the series is also developed. The solutions of fractional kinetic equations are presented in terms of the Mittag-Leffler function. The results established here are quite general in nature and capable of yielding both known and new results.

The amount of rainfall received over an area is an important factor in assessing availability of water to meet various demands for agriculture, industry, irrigation, generation of hydroelectricity and other human activities. In our study, we consider seasonal and periodic time series models for statistical analysis of rainfall data of Punjab, India. In this research paper we apply the Seasonal Autoregressive Integrated Moving Average and Periodic autoregressive model to analyse the rainfall data of Punjab. For evaluation of the model identification and periodic stationarity the statistical tool used are PeACF and PePACF. For model comparison we use Root mean square percentage error and forecast encompassing test. The results of this research will provide local authorities to develop strategic plans and appropriate use of available water resources.

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The Gaussian and non- Gaussian autoregressive models are used in this paper for analyzing time series data. The autoregressive time series models with various distributions are considered here for analyzing the annual rainfall of Punjab, India. Three different types of autoregressive models are applied here for analyzing data namely autoregressive model with Gaussian, Gamma and Laplace distribution. For the goodness of fit the chi - square test is applied and the best fitted distribution is obtained for the data. Next the stationarity of data is checked, after that models are applied on data for comparing three distributions of AR models and lastly the best fitted model is obtained. The residual checking of selected model is also discussed and forecast the best fitted model based on simulated response comparison.

The paper attempts forecasting the Cotton Growth area in Punjab and Haryana using the best fitted Auto-Regressive Integrated Moving Average (ARIMA) model. The time series data on area growth of cotton in Punjab and Haryana for the period of last 10 Years i.e. from 2012-13 to 2021-22 is analyzed for this study. The best models are selected by calculating Normalized BIC; Mean Absolute Percentage Error (MAPE) and maximum values of R . The study revealed that ARIMA (1,1,1) and ARIMA (0,1,1) are the best fitted models for forecasting Growth area of cotton in both states. The analysis shows an increasing trend in area of cotton for both the states Punjab and Haryana.

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This paper proposed a new model of quadratic fractional programming problem where our purpose is to study the quadratic fractional programming problem through fuzzy goal programming procedure by utilizing the bilevel linear programming. The bilevel is a class of multilevel optimization hierarchy with two decision levels and each objective function in both decision maker levels has fractional form with quadratic function in numerator as well as in denominator. In this paper we construct two bilevel quadratic programming problems from one bilevel quadratic fractional programming problem by separating the numerator and denominator in fractional objective function of each decision maker. Next our purpose isto solve both bilevel quadratic programming problems separately and thus to form a solution procedure for our proposed model which named as Bilevel Quadratic-Quadratic Fractional Programming Problem.

Chikungunya is a re-emerging arboviral disease in Asia and Africa infected by Aedes mosquitoes which had posed a global threat in several countries. Vector borne diseases are the primary cause of death in most of the world countries, hence it becomes pertinent to control these vector borne diseases. In this paper a mathematical model is provided by dividing it in four components namely Susceptible human, Exposed human, Infected human, Recovered human.The study is carried out on basic reproduction number and stability analysis. A mathematical model is developed for globally asymptotically stable disease-free equilibrium, when the associated reproduction number is less than unity. The aim of this study is to formulate a model where number of infectives will not change and the infection rate equals to the recovery rate by reaching stable endemic equilibrium point.