Page 21 - programme book

On the computable extension of fractional Volterra-type Integro-
differential Equations Involving Hilfer-Prabhakar Fractional Derivative

S.C. Pandey

Faculty of Mathematics and Computing, Department of Mathematics and Statistics, Banasthali Vidyapith,
Niwai, Rajasthan, India
sharedpandey@yahoo.co.in

Abstract. In the present article, an extension for the family of Volterra-type integro-differential
equations, involving a generalization of Hilfer fractional derivative with the Lorenzo-Hartley’s G-
function (LHGF) in the kernel, is proposed. A compact and computable solution of the considered
family of integro-differential equations is established in terms of an infinite series of LHGF. Further,
certain known and new special cases of the proposed family are also established. Furthermore, some
examples of the integro-differential equation are also discussed. Moreover, from the application point
of view, generalized fractional free-electron laser equations involving the Caputo and the Riemann-
Liouville fractional derivatives are determined as the classical cases of the studied family. Finally, the
graphical illustrations for the solutions of the studied generalized fractional free-electron laser equations
are demonstrated.
Keywords: Fractional-order integro-differential equation. Hilfer-Prabhakar fractional derivative.
Lorenzo Hartley’s G-function. Laplace transform.

Determinants of BMI for Indian Women: Estimates from NFHS - IV

Shalini Chandra

Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan-304022, INDIA

handrshalini@gmail.com

Abstract. The health status of women in a country determines the overall health of the whole country.
The basic factor responsible for health is nutrition. Thus, it is necessary to study nutrition and the factors
responsible. Studies have shown that the nutritional status of Indian women is one among the poorest.
In this paper, considering Body Mass Index (BMI) as an index to measure nutritional status, we study
the factors affecting BMI for Indian women. Data from National Family Health Survey (NFHS-4) have
been used for the analysis. The results of exploratory analysis revealed that the proportion of
underweight women was high among rural women and that of overweight/obesity was high among
urban women. With increase in age, education and wealth, BMI of women showed an increasing trend.
Women from Schedule tribes had smaller proportion of obesity than women of other castes. Christian
women had better BMI status than other religions. BMI improved with decrease in level of anemia.
North-Eastern women had the best BMI status among all zones. Furthermore, regression modeling was
performed to fit three different models to the data namely, Multiple Linear Regression model, Log-
Linear Regression Model and Multiple Linear Regression model with LASSO Regularisation, to
determine the most significant predictors of BMI. On comparing the above models using adjusted R2
to find the best model, Log-Linear model was observed to give the best fit.

Keywords: Women’s Health, NFHS, BMI, Linear Regression, Log-Linear, LASSO.