Rank

Legal Medicine, 2013

Mathematical Problems in Engineering, 2017

Optimal homotopy asymptotic method (OHAM) is proposed to solve linear and nonlinear systems of second-order boundary value problems. OHAM yields exact solutions in just single iteration depending upon the choice of selecting some part of or complete forcing function. Otherwise, it delivers numerical solutions in excellent agreement with exact solutions. Moreover, this procedure does not entail any discretization, linearization, or small perturbations and therefore reduces the computations a lot. Some examples are presented to establish the strength and applicability of this method. The results reveal that the method is very effective, straightforward, and simple to handle systems of boundary value problems.

The intersection of mathematics and software creates a point at which the right tools allows one to advance understanding of both fields in a synergistic way. Years of examination of this concept and multiple software development initiatives have lead to the current version of a software platform that lends itself to an optimal tool for achieving this goal. Two man-years of development efforts to date have evolved the platform in multiple areas of mathematics with software of a style that aids a student to improve understanding of development and architecture as well as the mathematics represented in the code. The areas of mathematics most heavily addressed are computation based on series, numerical calculus, and function interpolation. Additionally the software is coded in Java using generic types for the data operations so new abstracts for types can be added; currently implemented are domains for Real numbers, Complex numbers, and Prime numbers. Attempts are made to show the challenges presented by accuracy versus performance choices. At version 7.7 the documentation still resembles only notes of the intended final draft. Currently it is anticipated that an open source release of the software will be done concurrently with this finished document at some point in summer 2016. Input on this material from any source is welcome.

Experimental Neurology, 2007

Applied Numerical Mathematics, 1997

2020

The main aim of this article is the extension of Optimal Homotopy Asymptotic Method to the system of fractional order integro-differential equations. The systems of fractional order Volterra integro-differential equations (SFIDEs) are taken as test examples. The fractional order derivatives are defined in the Caputo fractional form and the optimal values of auxiliary constants are calculated using the well-known method of least squares. The results obtained by proposed scheme are very encouraging and show close resemblance with exact values. Hence it will be more appealing for the researchers to apply the proposed scheme to different fractional order systems arising in different fields of sciences especially in fluid dynamics and bio-engineering. Introduction Fractional calculus has been concerned with integration and differentiation of fractional (non-integer) order of the function. In recent years, fractional calculus has been revolutionized by its tremendous innovations, observed in different fields of science and technology, such as fractional dynamics, nonlinear oscillation, hereditary in mechanics of solids, visco-elastically damped structures, bio-engineering and continuum mechanics [1-6]. Therefore, researchers have paid enormous interest in this field. Dynamical behavior of mixed type lump solution [7], exact optical solution of perturbed nonlinear Schrödinger equation [8], nonlinear complex fractional emerging telecommunication model [9], explicit solution of nonlinear Zoomeron equation[10], optical soliton in nematic liquid crystals [11], two-hybrid technique coupled with integral transformation for caputo time fractional Navier-Stokes equation [12], Analysis of Fractionally-Damped generalized Bagley-Torvik equation [13], Brusselator reaction-diffusion system [14], Fractional order of biological system [15], time fractional lvancevic option pricing model [16], analysis of fractionally damped beams [17], model of vibration equation of large membranes [18], fractional Jeffrey fluid over inclined plane [19], thermal stratification of rotational second-grade fluid [20], long memory processes [21], heat-transfer properties of noble gases [22] and modelling the dynamic mechanical analysis [23]. A history of fractional differential operators can be found in [24]. Owing to its applications , researchers compel to extract its solutions, but exact solutions of all problems are difficult to find due to its nonlinearity. Therefore, researchers used analytical and numerical techniques for its approximate solutions. Numerical methods [25-28], perturbation methods [29-31], homotopy based method [32,33] and iterative techniques [34,35] are the main tools for obtaining the approximation of nonlinear problems. In the literature, researchers have used different techniques for the solution of fractional order integro-differential equations and their systems. Khan et al. implemented the Chebyshev wavelet method [36], Rahim et al. used the fractional alternative Leg-endre functions [37], Hamoud et al. applied the modified adomian decomposition method [38], Zedan et al. used the Chebyshev spectral method [39], and Zada et al. studied the impulsive coupled system [40]. The OHAM was introduced by Marinca et al. [41-43] for the solution of differential equations, and in a short period, different researchers have successfully implemented it for the solution of different problems

The Good Tourism Blog, 2023

Greg Richards thinks more of us should lift our gaze from our narrow academic, business, and local concerns. We should scan the horizons of what we (think we) know, and try harder to understand the primordial instinct we have to travel and the human incentives that drive the tourism industry. Professor Richards is the subject of the first in a series of Tourism’s Horizon Interviews. For this “Good Tourism” Insight, Jim Butcher summarises highlights of his in-depth interview with Prof Richards. [The full transcripts of the Tourism’s Horizon Interviews are available on Substack.]

The Journal of Gemmology, 2019

Cultures in Mountain Areas. Comparative Perspectives, edited by Tobias Boos, and Daniela Salvucci.. Bolzano: Bu.press, Bolzano University Press., 2022

A common idea in the southern Andes is that rituals to the mountains are part of a reciprocal pact between local populations and these powerful places, directed towards stabilising ecological systems and controlling resource management in their surrounding areas. However, human relations with mountains, especially the guardian mountains called uywiri, also serve as a crucial point of reference for metahuman powers of dominion that constrain human intervention in a certain environment, and which respond to the abuse of extracting too many minerals, or too many animals or plants, by devouring the humans within their domain. This Andean ethics concerning moral obligations towards the mountains, including the practices of rendering sacrifices, and its history, is my interest here. I compare these Andean practices, where mountains have mastery and ownership over the environment, with their lowland equivalents, and the proposal that these relations of power provide a missing link between regional notions of predation and of commensality through feeding.