EXISTENCE RESULTS OF SOLUTIONS FOR ANTI-PERIODIC FRACTIONAL LANGEVIN EQUATION

Ahmed Salem

doi:10.11948/20190419

2020 Volume 10 Issue 6

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Ahmed Salem. EXISTENCE RESULTS OF SOLUTIONS FOR ANTI-PERIODIC FRACTIONAL LANGEVIN EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2557-2574. doi: 10.11948/20190419

Citation:

Ahmed Salem. EXISTENCE RESULTS OF SOLUTIONS FOR ANTI-PERIODIC FRACTIONAL LANGEVIN EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2557-2574. doi: 10.11948/20190419

EXISTENCE RESULTS OF SOLUTIONS FOR ANTI-PERIODIC FRACTIONAL LANGEVIN EQUATION

Ahmed Salem

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

Author Bio: Email address: ahmedsalem74@hotmail.com (A. Salem)
Fund Project: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-638-130-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support

Abstract

Abstract

Recently, Khalili and Yadollahzadeh [9] have investigated the uniqueness and existence of solution $ u(t),\; t\in[0,1] $ for a class of nonlocal boundary conditions to fractional Langevin equation. The authors used the boundary condition $ u'(0) = 0 $ by incorrect method. In the current contribution, we show the correct method for using this condition and study the existence and uniqueness of solution for the same class of equation in slightly different form with anti-periodic and nonlocal integral boundary conditions as well as the boundary condition $ u'(0) = 0 $. An exemplar is provided to illustrate our results.
- Existence solution /
- fractional Langevin equation /
- anti-periodic condition
MSC: 26A33, 34A12, 34A08

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References

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