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Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions

Author

Listed:
  • Zhiyuan Yuan

    (School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China)

  • Luyao Wang

    (School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China)

  • Wenchang He

    (School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China)

  • Ning Cai

    (Department of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China)

  • Jia Mu

    (School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
    Key Laboratory of Streaming Data Computing Technologies and Application, Northwest Minzu University, Lanzhou 730030, China)

Abstract

We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by using fixed-point theorems, we establish the existence of mild solutions under more relaxed conditions.

Suggested Citation

  • Zhiyuan Yuan & Luyao Wang & Wenchang He & Ning Cai & Jia Mu, 2024. "Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1877-:d:1415968
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    References listed on IDEAS

    as
    1. Bedi, Pallavi & Kumar, Anoop & Khan, Aziz, 2021. "Controllability of neutral impulsive fractional differential equations with Atangana-Baleanu-Caputo derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Ben Makhlouf, Abdellatif & Mchiri, Lassaad, 2022. "Some results on the study of Caputo–Hadamard fractional stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Wang, Bo & Liu, Jinping & Alassafi, Madini O. & Alsaadi, Fawaz E. & Jahanshahi, Hadi & Bekiros, Stelios, 2022. "Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Rodrigo Ponce, 2016. "Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-15, September.
    5. Kaliraj, K. & Manjula, M. & Ravichandran, C., 2022. "New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    Full references (including those not matched with items on IDEAS)

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