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 view of some operators and their properties in terms of the Non-Newtonian Calculus [PDF]
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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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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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.
Asambo Awini Wilbert +2 more
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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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Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus
Foundations of Science, 2022 AbstractA class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For $$s\rightarrow \infty$$ s →
Michał Piotr Piłat
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Some new results on sequence spaces with respect to non-Newtonian calculus [PDF]
Journal of Inequalities and Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feyzi Basar
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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
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Fractional Hermite–Hadamard Inequalities in Non-Newtonian Calculus Focusing on h-GG-Convex Functions
International Journal of Mathematics and Mathematical SciencesThe aim of this paper is to develop new Hermite–Hadamard–type inequalities within the framework of fractional GG-multiplicative calculus. By employing the GG-multiplicative Riemann–Liouville fractional integral operators, we introduce a novel class of ...
Bouharket Benaissa +3 more
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On Fixed Point Results for Generalized Contractions in Non-Newtonian Metric Spaces
Cumhuriyet Science Journal, 2022 TThe work of non-Newtonian calculus was begun in 1972. This calculus provides a different area to the classical one. Non-Newtonian metric concept was defined in 2002 by Basar and Cakmak. Then Binbaşıoğlu et al.
Demet Binbaşıoğlu
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