A. G. Butkovskii, S. S. Postnov, E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation”, Avtomat. i Telemekh., 2013, no. 4, 3–42; Autom. Remote Control, 74:4 (2013), 543

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Avtomatika i Telemekhanika, 2013, Issue 4, Pages 3–42 (Mi at4973)

This article is cited in 42 scientific papers (total in 42 papers)

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Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation

A. G. Butkovskii^a, S. S. Postnov^a, E. A. Postnova^ab

^a Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
^b Moscow State University, Moscow, Russia

Full-text PDF (390 kB) Citations (42)

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Abstract: The review is devoted to using the fractional integro-differential calculus for description of the dynamics of various systems and control processes. Consideration was given to the basic notions of the fractional integro-differential calculus and the problem of interpretation of the fractional operators. Presented were examples of physical systems described in terms of the apparatus under consideration.

Presented by the member of Editorial Board: I. V. Roublev

Received: 05.03.2012

English version:
Automation and Remote Control, 2013, Volume 74, Issue 4, Pages 543–574
DOI: https://doi.org/10.1134/S0005117913040012

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. G. Butkovskii, S. S. Postnov, E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation”, Avtomat. i Telemekh., 2013, no. 4, 3–42; Autom. Remote Control, 74:4 (2013), 543–574

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/at4973

https://www.mathnet.ru/eng/at/y2013/i4/p3

Cycle of papers

Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation
A. G. Butkovskii, S. S. Postnov, E. A. Postnova
Avtomat. i Telemekh., 2013:4, 3–42
Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation
A. G. Butkovskii, S. S. Postnov, E. A. Postnova
Avtomat. i Telemekh., 2013:5, 3–34

This publication is cited in the following 42 articles:

Mohammed Al-Refai, Arran Fernandez, “Comparison principles for a class of general integro-differential inequalities with applications”, Comp. Appl. Math., 43:2 (2024)
Ricardo Almeida, “Euler–Lagrange-Type Equations for Functionals Involving Fractional Operators and Antiderivatives”, Mathematics, 11:14 (2023), 3208
M. I. Gomoyunov, N. Yu. Lukoyanov, “Optimal Feedback in a Linear–Quadratic Optimal Control Problem for a Fractional-Order System”, Diff Equat, 59:8 (2023), 1117
Faïçal Ndaïrou, Delfim F. M. Torres, “Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems”, Mathematics, 11:19 (2023), 4218
Vasily E. Tarasov, “General Fractional Calculus in Multi-Dimensional Space: Riesz Form”, Mathematics, 11:7 (2023), 1651
Alexandru Tudorache, Rodica Luca, “Positive Solutions for a System of Hadamard Fractional Boundary Value Problems on an Infinite Interval”, Axioms, 12:8 (2023), 793
Hatice Yalman Kosunalp, Mustafa Gulsu, “Towards solving linear fractional differential equations with Hermite operational matrix”, Adv. Studies: Euro-Tbilisi Math. J., 16:2 (2023)
Vasily E. Tarasov, “Entropy Interpretation of Hadamard Type Fractional Operators: Fractional Cumulative Entropy”, Entropy, 24:12 (2022), 1852
A. I. Fedotov, “Substantiation of a quadrature-difference method for solving integro-differential equations with derivatives of variable order”, Comput. Math. Math. Phys., 62:4 (2022), 548–563
Nazakat Nazeer, Muhammad Imran Asjad, Muhammad Khursheed Azam, Ali Akgül, “Study of Results of Katugampola Fractional Derivative and Chebyshev Inequailities”, Int. J. Appl. Comput. Math, 8:5 (2022)
Amjad Ali, Kamal Shah, Dildar Ahmad, Ghaus Ur Rahman, Nabil Mlaiki, Thabet Abdeljawad, “Study of multi term delay fractional order impulsive differential equation using fixed point approach”, MATH, 7:7 (2022), 11551
Ohud Almutairi, Adem K{\i}lıçman, “A Review of Hermite–Hadamard Inequality for α-Type Real-Valued Convex Functions”, Symmetry, 14:5 (2022), 840
Ufa Math. J., 13:1 (2021), 119–130
Zhao D., Yu G., Yu T., Zhang L., “A Probabilistic Interpretation of the Dzhrbashyan Fractional Integral”, Fractals-Complex Geom. Patterns Scaling Nat. Soc., 29:08 (2021), 2150269
Varghese V. Bhoyar S. Khalsa L., “Thermoelastic Response of a Nonhomogeneous Elliptic Plate in the Framework of Fractional Order Theory”, Arch. Appl. Mech., 91:7 (2021), 3223–3246
Yu. R. Agachev, A. V. Guskova, “Obobschennyi polinomialnyi metod resheniya zadachi tipa Koshi dlya odnogo drobno-differentsialnogo uravneniya”, Materialy XVII Vserossiiskoi molodezhnoi shkoly-konferentsii «Lobachevskie chteniya-2018», 23-28 noyabrya 2018 g., Kazan. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 176, VINITI RAN, M., 2020, 80–90
B. Bayraktar, “Some new generalizations of Hadamard–type Midpoint inequalities involving fractional integrals”, Probl. anal. Issues Anal., 9(27):3 (2020), 66–82
Ali A., Shah K., Abdeljawad T., Khan H., Khan A., “Study of Fractional Order Pantograph Type Impulsive Antiperiodic Boundary Value Problem”, Adv. Differ. Equ., 2020:1 (2020), 572
Redhwan S.S., Shaikh S.L., Abdo M.S., “Implicit Fractional Differential Equation With Anti-Periodic Boundary Condition Involving Caputo-Katugampola Type”, AIMS Math., 5:4 (2020), 3714–3730
Ayazyan G. Tausheva E., 2020 International Conference on Industrial Engineering, Applications and Manufacturing (Icieam), IEEE, 2020

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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