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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 5

Existence of solutions of BVPs for impulsive fractional Langevin equations involving Caputo fractional derivatives

Yuji LIU
Ravi AGARWAL
Pages
2451–2472
Publication Date
2022-11-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

New existence results for solutions of concerned problems are established.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The standard Caputo fractional derivative is generalized for the piecewise continuous functions.
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Key Findings & Data:A moregeneral boundary value problem for the impulsive Langevin fractional differential equation involving the Caputo fractionalderivatives is studied.
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Conclusion & Impact:New existence results for solutions of concerned problems are established.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The standard Caputo fractional derivative is generalized for the piecewise continuous functions. A moregeneral boundary value problem for the impulsive Langevin fractional differential equation involving the Caputo fractionalderivatives is studied. New existence results for solutions of concerned problems are established.

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Cite This Article

LIU, Y., AGARWAL, R. (2022). Existence of solutions of BVPs for impulsive fractional Langevin equations involving Caputo fractional derivatives. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 5, 2451–2472. https://ajindex.com/articles/607669

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References (17)

  1. Ahmad B, Eloe PW. A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices. Communications on Applied Nonlinear Analysis 2010; 17: 69-80
  2. Ahmad B, Nieto JJ. Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions. International Journal of Differential Equations 2010; 2010
  3. Ahmad B, Nieto JJ, Alsaedi A. A nonlocal three-point inclusion problem of Langevin equation with two different fractional orders. Advance in Difference Equations 2012; 54
  4. Ahmad B, Nieto JJ, Alsaedi A, El-Shahed M. A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Analysis Real World Applications 2012; 13: 599-606
  5. Coffey W, Kalmykov Y, Waldron J. The Langevin Equation, 2nd ed. Singapore: World Scientific, 2004
  6. Gambo Y, Jarad F, Baleanu D, Abdeljawad T. On Caputo modification of the Hadamard fractional derivative. Advance in Difference Equations 2014; 10
  7. Gao Z, Yu X, Wang J. Nonlocal problems for Langevin-type differential equations with two fractional-order derivatives. Boundary Value Problems 2016; 52
  8. Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations, in North- Holland Mathematics Studies, vol: 204, Amsterdam, the Netherlands: Elsevier Science B. V., 2006
  9. Kilbas AA, Marichev OI, Samko SG. Fractional Integral and Derivatives (Theory and Applications). Switzerland: Gordon and Breach, 1993
  10. Kilbas AA, Trujillo JJ. Differential equations of fractional order: methods resultsd and problems-I. Applicable Analysis 2010; 78(1): 153-192
  11. Lizana L, Ambjornsson T, Taloni A, Barkai E, Lomholt MA. Foundation of fractional Langevin equation: harmonization of a many-body problem. Physical Review E 2010; 81
  12. Mawhin J. Toplogical degree methods in nonlinear boundary value problems. In: NSFCBMS Regional Conference Series in Math; Providence, RI, USA: American Math Soc, 1979
  13. Nickolai K. Initial value problems of fractional order with fractional impulsive conditions. Results in Mathematics, 2013; 63: 1289-1310
  14. Ntouyas SK, Tariboon J. Fractional integral problems for Hadamard-Caputo fractional Langevin differential inclusions. Journal of Applied Mathematical Computations 2016; 51(1-2): 11-22
  15. Podlubny I. Fractional Differential Equations. Mathmatics in Science and Engineering. Vol
  16. San Diego, CA, USA: Academic Press, 1999
  17. Prabh