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A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative

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  • Logeswari, K.
  • Ravichandran, C.

Abstract

In this paper, we investigate a new fractional derivative with Mittag Leffler kernels (AB-derivative) to the fractional neutral integro-differential equations in Banach spaces. The results are based on fixed point theorems, then we implement a suitable examples and illustrate it by graphical methods with variation of fractional order.

Suggested Citation

  • Logeswari, K. & Ravichandran, C., 2020. "A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    • Handle: RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119319272
    DOI: 10.1016/j.physa.2019.123454
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    References listed on IDEAS

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    1. Yadav, Swati & Pandey, Rajesh K. & Shukla, Anil K., 2019. "Numerical approximations of Atangana–Baleanu Caputo derivative and its application," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 58-64.
    2. Alqahtani, Badr & Fulga, Andreea & Jarad, Fahd & Karapınar, Erdal, 2019. "Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 349-354.
    3. Khan, Hasib & Jarad, Fahd & Abdeljawad, Thabet & Khan, Aziz, 2019. "A singular ABC-fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 56-61.
    4. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    5. Khan, Aziz & Khan, Hasib & Gómez-Aguilar, J.F. & Abdeljawad, Thabet, 2019. "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 422-427.
    6. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.
    7. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
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    Cited by:

    1. Gao, Wei & Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D. G. & Kumar, Pushpendra, 2020. "A new study of unreported cases of 2019-nCOV epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Kucche, Kishor D. & Sutar, Sagar T., 2021. "Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Hammad, Hasanen A. & Alshehri, Maryam G., 2024. "Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Nisar, Kottakkaran Sooppy & Logeswari, K. & Ravichandran, C. & Sabarinathan, S., 2023. "New frame of fractional neutral ABC-derivative with IBC and mixed delay," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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