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
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A New Type of Sturm-Liouville Equation in the Non-Newtonian Calculus [PDF]
Journal of Function Spaces, 2021 In mathematical physics (such as the one-dimensional time-independent Schrödinger equation), Sturm-Liouville problems occur very frequently. We construct, with a different perspective, a Sturm-Liouville problem in multiplicative calculus by some ...
Sertac Goktas
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Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus [PDF]
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 Özlük
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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
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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.
Ünlüyol Erdal +2 more
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Convexity Properties in Non-Newtonian Calculus and Their Applications
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.
Asambo Awini Wilbert +2 more
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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
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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
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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
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Fractional analysis of unsteady squeezing flow of Casson fluid via homotopy perturbation method [PDF]
Scientific Reports, 2022 The objective of this article is to model and analyze unsteady squeezing flow of fractional MHD Casson fluid through a porous channel. Casson fluid model is significant in understanding the properties of non-Newtonian fluids such as blood flows, printing
Mubashir Qayyum +7 more
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