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Statistical convergence on non-Newtonian calculus
Journal of Analysis, 2023Statistical convergence has been considered by Zygmund and defined by Steinhaus and Fast. Then this concept has been characterized by Schoenberg. Since it has important applications in Fourier analysis, trigonometric series, Banach spaces, ergodic theory, number and measure theory, this concept has been handled by a new calculus known as non-Newtonian ...
Emrah Yilmaz +2 more
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Some applications of extended calculus to non-Newtonian flow in pipes
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2021Fractional and non-Newtonian calculus are an extension of classical calculus, usually known for providing new mathematical tools useful in science, developed from alternative approaches. Among fractional calculus, Riemann-Liouville and Caputo fractional derivatives have been the most popular operators employed in spite of their complexity. In this work,
Juan Stöckle
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Applications of non-Newtonian calculus for classical spaces and Orlicz functions
Afrika Matematika, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuldip Raj
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An introduction to non‐Newtonian calculus
International Journal of Mathematical Education in Science and Technology, 1979In this paper we explain the construction of an arbitrary non‐Newtonian calculus from two given complete ordered fields. We then discuss some features of a few specific non‐Newtonian calculi. And finally we speculate as to the eventual use of the non‐Newtonian calculi as alternatives to the classical calculus of Newton and Leibniz.
Michael Grossman
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From Non-Diophantine Arithmetic to Non-Newtonian Calculus
Non-Diophantine Arithmetics in Mathematics, Physics and Psychology, 2020exaly +3 more sources
Convex functions and some inequalities in terms of the Non-Newtonian Calculus
AIP Conference Proceedings, 2017Differentiation and integration are basic operations of calculus and analysis. Indeed, they are many versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz [1] gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into ...
Ünlüyol, Erdal +2 more
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Some geometric properties of the non-Newtonian sequence spaces lp (N)
Mathematica Slovaca, 2020In this paper, we generalize the concepts of convexity, strict convexity and uniform convexity in the sense of non-Newtonian calculus. The main aim of this study is to obtain the non-Newtonian convexity, non-Newtonian strict convexity and non-Newtonian ...
Nihan Güngör
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Communications on Applied Nonlinear Analysis
This research explores the recent advancements in mathematical modelling of heat transfer and fluid flows, emphasizing fractional calculus, non-Newtonian fluid dynamics, and nanofluid models. We discuss the use of fractional derivatives in modelling complex thermal and flow behaviours in various engineering contexts, including permeable surfaces and ...
Prabhat Kumar +6 more
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This research explores the recent advancements in mathematical modelling of heat transfer and fluid flows, emphasizing fractional calculus, non-Newtonian fluid dynamics, and nanofluid models. We discuss the use of fractional derivatives in modelling complex thermal and flow behaviours in various engineering contexts, including permeable surfaces and ...
Prabhat Kumar +6 more
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A note on linear non-Newtonian Volterra integral equations
Mathematical Sciences, 2021Nihan Güngör
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IEEE Congress on Evolutionary Computation, 2022
The variational approach of finding the extremum of an objective functional is an alternative approach to the solution of partial differential equations in mechanics of continua. The great challenge in the calculus of variations direct methods is to find
E. Kornaeva +4 more
semanticscholar +1 more source
The variational approach of finding the extremum of an objective functional is an alternative approach to the solution of partial differential equations in mechanics of continua. The great challenge in the calculus of variations direct methods is to find
E. Kornaeva +4 more
semanticscholar +1 more source