IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v165y2022ip1s0960077922009304.html
   My bibliography  Save this article

Manifestation of interval uncertainties for fractional differential equations under conformable derivative

Author

Listed:
  • Rahaman, Mostafijur
  • Mondal, Sankar Prasad
  • Alam, Shariful
  • Metwally, Ahmed Sayed M.
  • Salahshour, Soheil
  • Salimi, Mehdi
  • Ahmadian, Ali

Abstract

We propose a generalization of conformable calculus for Type-2 interval-valued functions. We investigated the differentiability and integrability properties of such functions. The conformable generalized Hukuhara (gH) differentiability of fractional order is introduced in this study. We prove a number of essential theorems on the conformable differentiability of the sum, gH difference, and product in a Type 2 interval setting. Furthermore, we define conformable Laplace transformation of Type-2 interval-valued functions. We interpret uncertain linear differential equations by using proposed theories. Several examples are given in detail to illustrate and clarify these rules and theorems. Applications to solving Type-2 interval differential equations with conformable derivatives are shown. Type-2 interval generalizes the interval uncertainty. On the other hand, conformable calculus extends the notion of integer calculus. This paper contributes a generalized theory that includes several existing results of classical integral and differential calculus and their conformable extensions in crisp and interval environments.

Suggested Citation

  • Rahaman, Mostafijur & Mondal, Sankar Prasad & Alam, Shariful & Metwally, Ahmed Sayed M. & Salahshour, Soheil & Salimi, Mehdi & Ahmadian, Ali, 2022. "Manifestation of interval uncertainties for fractional differential equations under conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009304
    DOI: 10.1016/j.chaos.2022.112751
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922009304
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112751?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    2. Dumitru Baleanu & Arran Fernandez, 2019. "On Fractional Operators and Their Classifications," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    3. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Julius Žilinskas & Ian David Lockhart Bogle, 2007. "A Survey of Methods for the Estimation Ranges of Functions Using Interval Arithmetic," Springer Optimization and Its Applications, in: Aimo Törn & Julius Žilinskas (ed.), Models and Algorithms for Global Optimization, pages 97-108, Springer.
    5. Jiang, C. & Han, X. & Liu, G.R. & Liu, G.P., 2008. "A nonlinear interval number programming method for uncertain optimization problems," European Journal of Operational Research, Elsevier, vol. 188(1), pages 1-13, July.
    6. Dumitru Baleanu & Arran Fernandez & Ali Akgül, 2020. "On a Fractional Operator Combining Proportional and Classical Differintegrals," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    7. Chenkuan Li & Kyle Clarkson, 2018. "Remarks on Convolutions and Fractional Derivative of Distributions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(1), pages 6-19, February.
    8. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shiri, Babak & Baleanu, Dumitru, 2023. "All linear fractional derivatives with power functions’ convolution kernel and interpolation properties," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Bezziou, Mohamed & Jebril, Iqbal & Dahmani, Zoubir, 2021. "A new nonlinear duffing system with sequential fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Izadi, Mohammad & Srivastava, H.M., 2021. "Numerical approximations to the nonlinear fractional-order Logistic population model with fractional-order Bessel and Legendre bases," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.
    5. Dumitru Baleanu & Arran Fernandez & Ali Akgül, 2020. "On a Fractional Operator Combining Proportional and Classical Differintegrals," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    6. Acay, Bahar & Inc, Mustafa & Mustapha, Umar Tasiu & Yusuf, Abdullahi, 2021. "Fractional dynamics and analysis for a lana fever infectious ailment with Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    7. Kucche, Kishor D. & Mali, Ashwini D. & Fernandez, Arran & Fahad, Hafiz Muhammad, 2022. "On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    8. Isah, Sunday Simon & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "On bivariate fractional calculus with general univariate analytic kernels," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    9. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    10. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    11. Mahdi Zarghami & Nasim Safari & Ferenc Szidarovszky & Shafiqul Islam, 2015. "Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4285-4303, September.
    12. Marina Plekhanova & Guzel Baybulatova, 2020. "Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems," Mathematics, MDPI, vol. 8(4), pages 1-9, April.
    13. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    14. Faïçal Ndaïrou & Delfim F. M. Torres, 2023. "Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems," Mathematics, MDPI, vol. 11(19), pages 1-12, October.
    15. Attia, Nourhane & Akgül, Ali & Seba, Djamila & Nour, Abdelkader, 2020. "An efficient numerical technique for a biological population model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    16. Gómez-Aguilar, J.F., 2020. "Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    17. Maike A. F. dos Santos, 2019. "Mittag–Leffler Memory Kernel in Lévy Flights," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    18. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    19. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    20. Jagdev Singh & Ahmed M. Alshehri & Shaher Momani & Samir Hadid & Devendra Kumar, 2022. "Computational Analysis of Fractional Diffusion Equations Occurring in Oil Pollution," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009304. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.