Shrinking Civic Space in Pakistan: Response and Strategies of the Civil Society

This paper focuses the issue of shrinking civic space in Pakistan. The study presents civil society activists’ responses on this issue, highlights their perception, present and future strategies to address this issue, and their effectiveness, as such, as well. Pakistan presents a unique case due to its involvement in the ‘war on terror’ and the consequences being faced by both the state and society at large. Present shrinking of civil society action is directly linked with it. In an attempt to grapple with the problems emerging from ‘war on terror’, the overgrown state is encroaching upon citizens’ space, thus denying the civil society to play its due role which can provide safety for the state as well. The preferred strategies of the NGOs include lobbying with parliamentarians and mobilizing the citizenry about the situation.

Numerical and Analytical Methods for Solving Fuzzy Differential Equations

This dissertation mainly intends to elucidate the concept of fuzzy theory on differential calculus. Differential calculus being the study of derivatives of functions at chosen input value has wide ranging practical applications to nearly all quantitative disciplines. Its advance development for fractional order derivatives has increased its significance in every area of science and engineering. While modeling ordinary and fractional differential equations of physical phenomenon, issues of every uncertainty is coped out by means of various theories, among which fuzzy theory is most popular. Specifically, fuzzy theory was designed to mathematically represent uncertainty and vagueness and to provide formalized tools for dealing with the imprecision intrinsic to many problems. This theory is proposed to make the membership function to operate over the range of real numbers [0, 1]. In this connection, here we have considered linear, non-linear, integer and fractional order differential models with uncertainty. Illustratively, exercises are constructed to present numerical-analytical solutions of initial value problems of fuzzy differential equations (FDEs) and fuzzy fractional differential equations (FFDEs). These differential equations are considered under strongly generalized Hukuhara differentiability. We proposed improved fractional Euler’s method (IFEM) and modified homotopy perturbation method (MHPM) for FFDEs. Also utilized max-min improved fractional Euler’s method and average improved fractional Euler’s method. Additionally, a novel operator method is investigated for the solution of linear FFDEs. Furthermore, we also dealt with the extension of applications of the new integral transform, Sumudu transform on FDEs and FFDEs. These methods are illustrated by solving several examples. Efficiency and exactness of results worked out are examined from the tables and graphs. The exact values are also simulated to compare and discuss the closeness and accuracy of approximations so obtained.