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Journal articles on the topic 'Differential calculus'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Tall, David, A. Avez, and D. Edmunds. "Differential Calculus." Mathematical Gazette 71, no. 455 (1987): 92. http://dx.doi.org/10.2307/3616332.

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2

Roebuck, D. J., and L. M. MacDonald. "Differential calculus." British Journal of Radiology 68, no. 813 (1995): 1037–38. http://dx.doi.org/10.1259/0007-1285-68-813-1037.

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3

Sommen, F. "Monogenic differential calculus." Transactions of the American Mathematical Society 326, no. 2 (1991): 613–32. http://dx.doi.org/10.1090/s0002-9947-1991-1012510-6.

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4

Steinbach, Bernd, and Christian Posthoff. "Boolean Differential Calculus." Synthesis Lectures on Digital Circuits and Systems 12, no. 1 (2017): 1–215. http://dx.doi.org/10.2200/s00766ed1v01y201704dcs052.

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5

Mott, Richard. "Genetic differential calculus." Nature Genetics 47, no. 9 (2015): 965–66. http://dx.doi.org/10.1038/ng.3384.

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6

Samborskii, S. N. "Nonsmooth differential calculus." Doklady Mathematics 81, no. 2 (2010): 262–64. http://dx.doi.org/10.1134/s1064562410020274.

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7

Filippov, A. T., A. P. Isaev, and A. B. Kurdikov. "Paragrassmann differential calculus." Theoretical and Mathematical Physics 94, no. 2 (1993): 150–65. http://dx.doi.org/10.1007/bf01019327.

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8

Hitzer, Eckhard M. S. "Multivector differential calculus." Advances in Applied Clifford Algebras 12, no. 2 (2002): 135–82. http://dx.doi.org/10.1007/bf03161244.

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9

Mwinken, Delphin. "The Interconnection Between Calculus of Variations, Partial Differential Equations and Differential Geometry." Selecciones Matemáticas 11, no. 02 (2024): 393–408. https://doi.org/10.17268/sel.mat.2024.02.11.

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Calculus of variations is a fundamental mathematical discipline focused on optimizing functionals, which map sets of functions to real numbers. This field is essential for numerous applications, including the formulation and solution of partial differential equations (PDEs) and the study of differential geometry. In PDEs, calculus of variations provides methods to find functions that minimize energy functionals, leading to solutions of various physical problems. In differential geometry, it helps understand the properties of curves and surfaces, such as geodesics, by minimizing arc-length func

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10

Jain, Pankaj, Chandrani Basu, and Vivek Panwar. "Reduced $pq$-Differential Transform Method and Applications." Journal of Inequalities and Special Functions 13, no. 1 (2022): 24–40. http://dx.doi.org/10.54379/jiasf-2022-1-3.

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In this paper, Reduced Differential Transform method in the framework of (p, q)-calculus, denoted by Rp,qDT , has been introduced and applied in solving a variety of differential equations such as diffusion equation, 2Dwave equation, K-dV equation, Burgers equations and Ito system. While the diffusion equation has been studied for the special case p = 1, i.e., in the framework of q-calculus, the other equations have not been studied even in q-calculus.

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11

Kalanov, Temur Z. "Differential Calculus: a gross error in mathematics ∗." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 42, no. 2 (2023): 109–21. http://dx.doi.org/10.48165/bpas.2023.42e.2.2.

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A detailed proof of the incorrectness of the foundations of the differential calculus is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: differential calculus represents a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable results: (1) the standard theory of infinitesimals and the theory of limits underlying the differential calculus are gross errors. The main error is that infinitesimal (infinitely decreasing) quantities

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12

Flowers, M. J., and R. L. Wallis. "Differential and Integral Calculus." Mathematical Gazette 69, no. 447 (1985): 58. http://dx.doi.org/10.2307/3616467.

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13

Ehrhard, Thomas, and Laurent Regnier. "The differential lambda-calculus." Theoretical Computer Science 309, no. 1-3 (2003): 1–41. http://dx.doi.org/10.1016/s0304-3975(03)00392-x.

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14

Vaux, Lionel. "The differential λμ-calculus". Theoretical Computer Science 379, № 1-2 (2007): 166–209. http://dx.doi.org/10.1016/j.tcs.2007.02.028.

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15

Ashlock, Daniel. "Fast Start Differential Calculus." Synthesis Lectures on Mathematics and Statistics 11, no. 5 (2019): 1–236. http://dx.doi.org/10.2200/s00943ed1v01y201908mas028.

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16

Illusie, Luc. "Grothendieck and differential calculus." Comptes Rendus. Mathématique 363, G9 (2025): 829–41. https://doi.org/10.5802/crmath.764.

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I discuss some of the contributions that Grothendieck brought to differential calculus in the 1960s (infinitesimal neighborhoods, algebraic de Rham cohomology, crystalline cohomology) and sketch a few recent developments.

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17

Sardanashvily, G., and W. Wachowski. "Differential Calculus onN-Graded Manifolds." Journal of Mathematics 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/8271562.

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The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, overN-graded commutative rings and onN-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and onZ2-graded manifolds. We follow the notion of anN-graded manifold as a local-ringed space whose body is a smooth manifoldZ. A key point is that the graded derivation module of the structure ring of graded functions

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18

JUMARIE, GUY. "RIEMANN-CHRISTOFFEL TENSOR IN DIFFERENTIAL GEOMETRY OF FRACTIONAL ORDER APPLICATION TO FRACTAL SPACE-TIME." Fractals 21, no. 01 (2013): 1350004. http://dx.doi.org/10.1142/s0218348x13500047.

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By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geome

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19

PARVATE, ABHAY, and A. D. GANGAL. "CALCULUS ON FRACTAL SUBSETS OF REAL LINE — II: CONJUGACY WITH ORDINARY CALCULUS." Fractals 19, no. 03 (2011): 271–90. http://dx.doi.org/10.1142/s0218348x11005440.

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Calculus on fractals, or Fα-calculus, developed in a previous paper, is a calculus based fractals F ⊂ R, and involves Fα-integral and Fα-derivative of orders α, 0 < α ≤ 1, where α is the dimension of F. The Fα-integral is suitable for integrating functions with fractal support of dimension α, while the Fα-derivative enables us to differentiate functions like the Cantor staircase. Several results in Fα-calculus are analogous to corresponding results in ordinary calculus, such as the Leibniz rule, fundamental theorems, etc. The functions like the Cantor staircase function occur naturally as s

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20

Lazopoulos, Konstantinos A. "On Λ-Fractional Differential Equations". Foundations 2, № 3 (2022): 726–45. http://dx.doi.org/10.3390/foundations2030050.

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Λ-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence, all the sources of generating fractional differential equations, such as fractional differential geometry, the fractional calculus of variations, and the fractional field theory, are not mathematically accurate. Nevertheless, the Λ-fractional deriv

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21

Feng, Xiaobing, and Mitchell Sutton. "A new theory of fractional differential calculus." Analysis and Applications 19, no. 04 (2021): 715–50. http://dx.doi.org/10.1142/s0219530521500019.

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This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions and characterize what functions are fractionally differentiable. Various calculus rules including a fundamental theorem calculus, product and chain rules, and integration by parts formulas are established for weak fractional derivatives. Additionally, relationsh

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22

MANZONETTO, GIULIO. "What is a categorical model of the differential and the resource λ-calculi?" Mathematical Structures in Computer Science 22, № 3 (2012): 451–520. http://dx.doi.org/10.1017/s0960129511000594.

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The differential λ-calculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows the application of a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitable primitives to handle explicitly the resources used by a program during its execution. The differential operator also allows us to write the full Taylor expansion of a program. Through this expansion, every program can be decomposed into an infinite sum (representing non-deterministic cho

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23

Márquez Albés, Ignacio, and F. Adrián F. Tojo. "Displacement Calculus." Mathematics 8, no. 3 (2020): 419. http://dx.doi.org/10.3390/math8030419.

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In this work, we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on to differentiation and integration. We find interesting notions on the way, such as the integral with respect to a path of measures or the displacement derivative. We relate both of these two concepts by a Fundamental Theorem of Calculus. Finally, we develop the necessary framework in order to study displacement equations by relating them to Stieltjes diff

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24

Shodiyev, Erkin Oltiboyevich Dursoatov Mansur Bozor oʻgʻli. "CRITICAL ANALYSIS OF THE FUNDAMENTALS OF DIFFERENTIAL AND INTEGRAL CALCULUS." ACADEMIC RESEARCH IN MODERN SCIENCE 1, no. 15 (2022): 39–42. https://doi.org/10.5281/zenodo.7151555.

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The development and content of integral calculus is inextricably linked with the development and content of differential calculus. This article provides the necessary information about the critical analysis of the fundamentals of differential and integral calculus.

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25

Burton, D. A. "A primer on exterior differential calculus." Theoretical and Applied Mechanics, no. 30 (2003): 85–162. http://dx.doi.org/10.2298/tam0302085b.

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A pedagogical application-oriented introduction to the cal?culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con?nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi?tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples

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26

Ahmad, Imtiaz, Rashid Jan, Md Nur Alam, and Muhammad Nawaz Khan. "Novel Techniques for Classifying Exotic Spheres in High Dimensions." Babylonian Journal of Mathematics 2023 (July 18, 2023): 36–39. http://dx.doi.org/10.58496/bjm/2023/007.

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Discrete calculus deals with developing the concepts and techniques of differential and integral calculus in a discrete setting, often using difference equations and discrete function spaces. This paper explores how differential-difference algebra can provide an algebraic framework for advancing discrete calculus. Differential-difference algebra studies algebraic structures equipped with both differential and difference operators. These hybrid algebraic systems unify continuous and discrete analogues of derivatives and shifts. This allows the development of general theorems and properties that

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27

RODRÍGUEZ PERALTA, María de Lourdes, Juan Salvador NAMBO de LOS SANTOS, and Paula Flora ANICETO VARGAS. "Mathematics in the Classroom: Conceptual Cartography of Differential Calculus." Revista Romaneasca pentru Educatie Multidimensionala 7, no. 2 (2015): 47–54. http://dx.doi.org/10.18662/rrem/2015.0702.04.

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28

NAKAMURA, Yayoi, and Shinichi TAJIMA. "RESIDUE CALCULUS WITH DIFFERENTIAL OPERATOR." Kyushu Journal of Mathematics 54, no. 1 (2000): 127–38. http://dx.doi.org/10.2206/kyushujm.54.127.

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29

Hobbs, D. "Differential calculus: concepts and notation." Teaching Mathematics and its Applications 16, no. 4 (1997): 181–91. http://dx.doi.org/10.1093/teamat/16.4.181.

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30

Zharinov, Victor V. "Operational calculus in differential algebras∗." Integral Transforms and Special Functions 7, no. 1-2 (1998): 145–58. http://dx.doi.org/10.1080/10652469808819192.

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31

Parisi, Francesco, and Jonathan Klick. "The Differential Calculus of Consent." Journal of Public Finance and Public Choice 20, no. 2 (2002): 115–24. http://dx.doi.org/10.1332/251569202x15665366114888.

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Abstract Existing treatments of the choice of an optimal voting rule ignore the effects of the rule on political bargaining. Specifically, more stringent majority requirements reduce intra-coalitional free riding in political compromise, leading to greater gains from political trade. Once this benefit of increasing the vote share necessary to enact a proposal is recognized, we suggest that the optimal voting rule in the presence of transactions costs will actually be closer to unanimity than the optimal majority derived by Buchanan - Tullock [1962].

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32

Wand, M. P. "Vector Differential Calculus in Statistics." American Statistician 56, no. 1 (2002): 55–62. http://dx.doi.org/10.1198/000313002753631376.

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33

Hilger, Stefan. "Differential and difference calculus — Unified!" Nonlinear Analysis: Theory, Methods & Applications 30, no. 5 (1997): 2683–94. http://dx.doi.org/10.1016/s0362-546x(96)00204-0.

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34

Schremmer, Francesca, and Alain Schremmer. "The Differential Calculus as Language." Bulletin of Science, Technology & Society 8, no. 4 (1988): 411–18. http://dx.doi.org/10.1177/027046768800800410.

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35

Dubois-Violette, Michel, and Richard Kerner. "Universal ZN-graded differential calculus." Journal of Geometry and Physics 23, no. 3-4 (1997): 235–46. http://dx.doi.org/10.1016/s0393-0440(97)80002-2.

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36

Akulov, V. P., S. A. Duplij, and V. V. Chitov. "Differential calculus forq-deformed twistors." Theoretical and Mathematical Physics 115, no. 2 (1998): 513–19. http://dx.doi.org/10.1007/bf02575451.

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37

Aragona, J., R. Fernandez, and S. O. Juriaans. "A Discontinuous Colombeau Differential Calculus." Monatshefte f�r Mathematik 144, no. 1 (2004): 13–29. http://dx.doi.org/10.1007/s00605-004-0257-0.

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38

ÇELİK, Salih, and İlknur TEMLİ. "Covariant differential calculus on SP2j1." TURKISH JOURNAL OF MATHEMATICS 43, no. 2 (2019): 916–29. http://dx.doi.org/10.3906/mat-1812-92.

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39

Diao, Peter, Dominique Guillot, Apoorva Khare, and Bala Rajaratnam. "Differential calculus on graphon space." Journal of Combinatorial Theory, Series A 133 (July 2015): 183–227. http://dx.doi.org/10.1016/j.jcta.2015.02.006.

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40

Alzaareer, Hamza. "Differential calculus on multiple products." Indagationes Mathematicae 30, no. 6 (2019): 1036–60. http://dx.doi.org/10.1016/j.indag.2019.07.008.

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41

Podleś, Piotr. "Differential calculus on quantum spheres." Letters in Mathematical Physics 18, no. 2 (1989): 107–19. http://dx.doi.org/10.1007/bf00401865.

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42

PAN, XUEZAI, RONGFEI XU, XUDONG SHANG, and MINGGANG WANG. "THE PROPERTIES OF FRACTIONAL ORDER CALCULUS OF FRACTAL INTERPOLATION FUNCTION OF BROKEN LINE SEGMENTS." Fractals 26, no. 03 (2018): 1850031. http://dx.doi.org/10.1142/s0218348x18500317.

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In order to research the properties of the fractional order calculus of broken line segments’ fractal interpolation function (FIF) generated by the linear iterated function system (IFS), the concepts of the Riemann–Liouville fractional order calculus and the method of the IFS are used to prove the properties of the fractional calculus of the broken line segments’ FIF generated by the linear IFS. There are two conclusions as follows. First, the fractional order integral of the broken line segments’ FIF formed by the linear IFS is continuous and first-order differentiable on the closed interval

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43

Zhelobenko, D. P. "Differential operators and differential calculus in quantum groups." Izvestiya: Mathematics 62, no. 4 (1998): 673–94. http://dx.doi.org/10.1070/im1998v062n04abeh000191.

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44

Harrison, J. "Operator Calculus of Differential Chains and Differential Forms." Journal of Geometric Analysis 25, no. 1 (2013): 357–420. http://dx.doi.org/10.1007/s12220-013-9433-6.

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45

MAGNANI, VALENTINO. "TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS." Journal of the Australian Mathematical Society 95, no. 1 (2013): 76–128. http://dx.doi.org/10.1017/s1446788713000098.

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AbstractWe study graded group-valued continuously differentiable mappings defined on stratified groups, where differentiability is understood with respect to the group structure. We characterize these mappings by a system of nonlinear first-order PDEs, establishing a quantitative estimate for their difference quotient. This provides us with a mean value estimate that allows us to prove both the inverse mapping theorem and the implicit function theorem. The latter theorem also relies on the fact that the differential admits a proper factorization of the domain into a suitable inner semidirect p

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46

Tunç, Cemil, Jen-Chih Yao, Mouffak Benchohra, and Ahmed M. A. El-Sayed. "Editorial for the Special Issue of “Fractional Differential and Fractional Integro-Differential Equations: Qualitative Theory, Numerical Simulations, and Symmetry Analysis”." Symmetry 16, no. 9 (2024): 1193. http://dx.doi.org/10.3390/sym16091193.

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47

MADORE, J. "ON THE RESOLUTION OF SPACE-TIME SINGULARITIES." International Journal of Modern Physics B 14, no. 22n23 (2000): 2419–25. http://dx.doi.org/10.1142/s0217979200001941.

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In previous articles it has been argued that a differential calculus over a noncommutative algebra uniquely determines a gravitational field in the commutative limit and that there is a unique metric which remains as a classical "shadow". Some examples were given of metrics which resulted from a given algebra and given differential calculus. Here we aboard the inverse problem, that of constructing the algebra and the differential calculus from the classical metric.

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48

Alarifi, Najla M., and Rabha W. Ibrahim. "Specific Classes of Analytic Functions Communicated with a Q-Differential Operator Including a Generalized Hypergeometic Function." Fractal and Fractional 6, no. 10 (2022): 545. http://dx.doi.org/10.3390/fractalfract6100545.

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A special function is a function that is typically entitled after an early scientist who studied its features and has a specific application in mathematical physics or another area of mathematics. There are a few significant examples, including the hypergeometric function and its unique species. These types of special functions are generalized by fractional calculus, fractal, q-calculus, (q,p)-calculus and k-calculus. By engaging the notion of q-fractional calculus (QFC), we investigate the geometric properties of the generalized Prabhakar fractional differential operator in the open unit disk

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49

Boccuto, Antonio, and Domenico Candeloro. "Differential Calculus in Riesz Spaces and Applications to g-Calculus." Mediterranean Journal of Mathematics 8, no. 3 (2010): 315–29. http://dx.doi.org/10.1007/s00009-010-0072-x.

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50

Witt, I. "A Calculus for Classical Pseudo - Differential Operators with Non -Smooth Symbols Witt, Pseudo-Differential Calculus." Mathematische Nachrichten 194, no. 1 (1998): 239–84. http://dx.doi.org/10.1002/mana.19981940116.

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