On a Non-Newtonian Calculus of Variations [PDF]
Axioms, 2021 The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals.
Delfim F. M. Torres
exaly +4 more sources
A New View of Some Operators and Their Properties in Terms of the Non-Newtonian Calculus
Topological Algebra and Its Applications, 2017 Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively.
Imdat İşcan +2 more
exaly +4 more sources
Generalized Runge-Kutta Method With Respect to the Non-Newtonian Calculus
Abstract and Applied Analysis, 2015 Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian
Uğur Kadak, Muharrem Ozluk
exaly +3 more sources
Convexity Properties in Non-Newtonian Calculus and Their Applications [PDF]
European Journal of Mathematical AnalysisThe study presented some results on convexity properties in non-Newtonian calculus. Also presented is the Jensen-Steffensen inequality in non-Newtonian calculus and some applications. The research was mainly on positive real numbers.
Benedict Barnes
exaly +4 more sources
Unsteady two dimensional flow of non-newtönian fractional Casson fluid for an edge with heated boundaries [PDF]
Scientific ReportsThis study explores the transient flow and thermal behavior of incompressible non-Newtonian fluids, with a particular emphasis on Casson and fractional Casson models, which are widely applied in blood flow, lubricants, and polymer processing.
Sohail Nadeem +4 more
doaj +2 more sources
Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers [PDF]
Abstract and Applied Analysis, 2014 This paper is devoted to investigate some characteristic features of complex numbers and functions in terms of non-Newtonian calculus. Following Grossman and Katz, (Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972), we construct the ...
Ahmet Faruk Çakmak, Feyzi Başar
doaj +2 more sources
Unifying Aspects of Generalized Calculus
Entropy, 2020 Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory.
Marek Czachor
exaly +3 more sources
On the Relativity of Quantumness as Implied by Relativity of Arithmetic and Probability [PDF]
EntropyA hierarchical structure of isomorphic arithmetics is defined by a bijection gR:R→R. It entails a hierarchy of probabilistic models, with probabilities pk=gk(p), where g is the restriction of gR to the interval [0,1], gk is the kth iterate of g, and k is
Marek Czachor
doaj +2 more sources
Fractional-order modelling and analytical solutions for MHD casson fluid flow in an inclined channel with heat and mass transfer [PDF]
Scientific ReportsThis study investigates the unsteady magnetohydrodynamic (MHD) flow of a Casson fluid in an inclined channel using a fractional calculus framework.
Maher Alwuthaynani +5 more
doaj +2 more sources
A new view of spaces and their properties in the sense of non-Newtonian measure. [PDF]
PLoS ONEThis study presents a novel approach to metric spaces through the lens of geometric calculus, redefining traditional structures with new operations and properties derived from non-Newtonian measures.
Amer Darweesh +3 more
doaj +2 more sources