Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
Electric Powertrains and Energy Systems 2025 | 26 + 27 March 2025

19th International MTZ Congress on Future Powertrains

Take this opportunity to attend the conference. Experts from the automotive industry, energy providers, and grid operators will meet up with representatives from politics and science to discuss important topics for this sector.
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2024 | OriginalPaper | Chapter

On Conformable Fractional Riesz Bounded \(\user2{ p} -\) Variation of Order \(- \user2{ \alpha }\)

Authors : Supriyadi Wibowo, Christiana Rini Indrati

Published in: Applied and Computational Mathematics

Publisher: Springer Nature Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, inspired by the concept of conformable fractional (CF) derivative of order \(\alpha\) with the definitions of Riesz bounded \(p -\) variation and Lipschitz continuous function, we introduce the new definitions of CF Riesz bounded variation and CF Lipschitz continuous function, respectively. Furthermore, we give some of its important properties and the relationships among those functions. In particular, the following chain of inclusions holds:
$$\rm{\mathbb{D}}^{\alpha} \left[ {a,b} \right] \subset \rm{{\mathbb{L}}{\mathbb{I}}{\mathbb{P}}}^{\alpha} \left[ {a,b} \right] \subset \rm{{\mathbb{B}}{\mathbb{V}}}^{\alpha,p} \left[ {a,b} \right] \subset \rm{{\mathbb{B}}{\mathbb{V}}}^{\alpha,q} \left[ {a,b} \right].$$
where \(\alpha \in \left( {0,} \right.\left. 1 \right]\) and \(p,q \in \left( {1,\infty } \right)\) where \(q < p\).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter The Vertex Degree of Relative G-Noncommuting Graph of the Dihedral Groups
next chapter The Wiener Index, the Harmonic Index, and the Graph Representation of the Prime Ideal Graph for the Integers Modulo Rings with Prime Power Order
Literature
1.
2.
Agarwal, R.P., Lakshmikantham, V., Nieto, J.J.: On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. Theory Methods Appl. 72(6), 2859–2862 (2010)MathSciNetCrossRef
3.
4.
Almeida, R., Guzowska, M., Odzijewicz, T.: A remark on local fractional calculus and ordinary derivatives. Open Mathematics 14(1), 1122–1124 (2016)MathSciNetCrossRef
5.
Atangana, A., Baleanu, D., Alsaedi, A.: New properties of conformable derivative. Open Math. 13(1), 889–898 (2015)MathSciNetCrossRef
6.
Azouz, F., Boucenna, D., Ben Makhlouf, A., Mchiri, L., Benchaabane, A.: Controllability of differential systems with the general conformable derivative. Complexity, pp. 1–11 (2021)
7.
Castillo, R.E., Guzmán, O.M., Rafeiro, H.: Variable exponent bounded variation spaces in the Riesz sense. Nonlinear Anal. 132, 173–182 (2016)MathSciNetCrossRef
8.
El-Ajou, A.: A modification to the conformable fractional calculus with some applications. Alex. Eng. J. 59(4), 2239–2249 (2020)CrossRef
9.
10.
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRef
11.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
12.
Luchko, Y.: Operational method in fractional calculus. Fract. Calc. Appl. Anal 2(4), 463–488 (1999)MathSciNet
13.
Reinwand, S.: Functions of Bounded Variation: Theory • Methods • Applications. Cuvillier Verlag, Göttingen (2021)
14.
15.
Rosa, W., Weberszpil, J.: Dual conformable derivative: definition, simple properties and perspectives for applications. Chaos, Solitons Fractals 117, 137–141 (2018)MathSciNetCrossRef
16.
17.
Uchaikin, V.V.: Fractional Derivatives for Physicists and Engineers, vol. 2. Springer, Berlin (2013)
18.
Valério, D., Machado, J.T., Kiryakova, V.: Some pioneers of the applications of fractional calculus. Fractional Calculus Appl. Anal. 17(2), 552–578 (2014)MathSciNetCrossRef
19.
Wiener, N.: The quadratic variation of a function and its fourier coefficients. J. Math. Phys. Massachusetts 3, 72–94 (1924)CrossRef
20.
Yang, X.J., Machado, J.T., Hristov, J.: Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. Nonlinear Dyn. 84(1), 3–7 (2016)MathSciNetCrossRef
21.
Zhao, D., Luo, M.: General conformable fractional derivative and its physical interpretation. Calcolo 54(3), 903–917 (2017)MathSciNetCrossRef
22.
Zhao, D., Pan, X., Luo, M.: A new framework for multivariate general conformable fractional calculus and potential applications. Physica A 510, 271–280 (2018)MathSciNetCrossRef
Metadata
Title
On Conformable Fractional Riesz Bounded Variation of Order
Authors
Supriyadi Wibowo
Christiana Rini Indrati
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Applied and Computational Mathematics

Print ISBN: 978-981-9721-35-1

Electronic ISBN: 978-981-9721-36-8

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-2136-8_27

Premium Partners

    Image Credits