journal article Jan 01, 2021

Nonlocal coupled system for $ \psi $-Hilfer fractional order Langevin equations

View at Publisher Save 10.3934/math.2021566
Topics

No keywords indexed for this article. Browse by subject →

References
29
[1]
K. Diethelm, <i>The Analysis of Fractional Differential Equations</i>, Lecture Notes in Mathematics, Springer, New York, 2010. 10.1007/978-3-642-14574-2
[2]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, <i>Theory and Applications of the Fractional Differential Equations</i>, North-Holland Mathematics Studies, 204, 2006.
[3]
V. Lakshmikantham, S. Leela, J. V. Devi, <i>Theory of Fractional Dynamic Systems</i>, Cambridge Scientific Publishers, 2009.
[4]
K. S. Miller, B. Ross, <i>An Introduction to the Fractional Calculus and Differential Equations</i>, John Wiley, NewYork, 1993.
[5]
I. Podlubny, <i>Fractional Differential Equations</i>, Academic Press, New York, 1999.
[6]
S. G. Samko, A. A. Kilbas, O. I. Marichev, <i>Fractional Integrals and Derivatives</i>, Gordon and Breach Science, Yverdon, 1993.
[7]
Y. Zhou, <i>Basic Theory of Fractional Differential Equations</i>, World Scientific, Singapore, 2014. 10.1142/9069
[8]
B. Ahmad, A. Alsaedi, S.K. Ntouyas, J. Tariboon, <i>Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities</i>, Springer, Cham, Switzerland, 2017. 10.1007/978-3-319-52141-1
[9]
R. Hilfer, <i>Applications of Fractional Calculus in Physics</i>, World Scientific, Singapore, 2000. 10.1142/3779
[10]
R. Hilfer, Experimental evidence for fractional time evolution in glass forming materials, <i>J. Chem. Phys.</i>, <b>284</b> (2002), 399–408. 10.1016/s0301-0104(02)00670-5
[11]
R. Hilfer, Y. Luchko, Z. Tomovski, Operational method for the solution of fractional differential equations with generalized Riemann-Liouvill fractional derivatives, <i>Frac. Calc. Appl. Anal.</i>, <b>12</b> (2009), 299–318.
[12]
R. Almeida, A Caputo fractional derivative of a function with respect to another function, <i>Commun. Nonlinear Sci. Numer. Simulat.</i>, <b>44</b> (2017), 460–481. 10.1016/j.cnsns.2016.09.006
[13]
On the ψ -Hilfer fractional derivative

J. Vanterler da C. Sousa, E. Capelas de Oliveira

Communications in Nonlinear Science and Numerical... 10.1016/j.cnsns.2018.01.005
[14]
J. Vanterler da C. Sousa, E. Capelas de Oliveira, Leibniz type rule: $\psi$-Hilfer fractional operator, <i>Commun. Nonlinear Sci. Numer. Simul.</i>, <b>77</b> (2019), 305–311. 10.1016/j.cnsns.2019.05.003
[15]
J. Vanterler da C. Sousa, E. Capelas de Oliveira, Ulam-Hyers stability of a nonlinear fractional Volterra integro-differential equation, <i>Appl. Math. Lett.</i>, <b>81</b> (2018), 50–56. 10.1016/j.aml.2018.01.016
[16]
K. M. Furati, N. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, <i>Comput. Math. Appl.</i>, <b>64</b> (2012), 1616–1626. 10.1016/j.camwa.2012.01.009
[17]
H. Gu, J. J. Trujillo, Existence of mild solution for evolution equation with Hilfer fractional derivative, <i>Appl. Math. Comput.</i>, <b>257</b> (2015), 344–354. 10.1016/j.amc.2014.10.083
[18]
Nonlocal initial value problems for differential equations with Hilfer fractional derivative

Yuruo Zhang

Applied Mathematics and Computation 10.1016/j.amc.2015.05.144
[19]
S. Asawasamrit, A. Kijjathanakorn, S. K. Ntouyas, J. Tariboon, Nonlocal boundary value problems for Hilfer fractional differential equations, <i>Bull. Korean Math. Soc.</i>, <b>55</b> (2018), 1639–1657.
[20]
A. Mali, K. Kucche, Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations, <i>Math. Meth. Appl. Sci.</i>, <b>43</b> (2020), 8608–8631. 10.1002/mma.6521
[21]
S. K. Ntouyas, D. Vivek, Existence and uniqueness results for sequential $\psi$-Hilfer fractional differential equations with multi-point boundary conditions, <i>Acta Mathematica Universitatis Comenianae</i>, <b>90</b> (2021), 171–185.
[22]
W. T. Coffey, Yu. P. Kalmykov, J. T. Waldron, <i>The Langevin Equation</i>, second ed., World Scientific, Singapore, 2004. 10.1142/5343
[23]
A. Alsaedi, S. K. Ntouyas, B. Ahmad, Existence results for Langevin fractional differential inclusions involving two fractional orders with four-point multi-term fractional integral boundary conditions, <i>Abstr. Appl. Anal.</i>, <b>2013</b> (2013), 1–17. 10.1155/2013/869837
[24]
J. Tariboon, S. K. Ntouyas, Nonlinear second-order impulsive $q$-difference Langevin equation with boundary conditions, <i>Bound. Value Probl.</i>, <b>2014</b> (2014), 85. 10.1186/1687-2770-2014-85
[25]
J. Tariboon, S. K. Ntouyas, C. Thaiprayoon, Nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions, <i>Adv. Math. Phys.</i>, <b>2014</b> (2014), 1–15. 10.1155/2014/372749
[26]
Ch. Nuchpong, S. K. Ntouyas, D. Vivek, J. Tariboon, Nonlocal boundary value problems for $\psi$-Hilfer fractional-order Langevin equations, <i>Bound. Value Probl.</i>, <b>2021</b> (2021), 1–12. 10.1186/s13661-020-01478-2
[27]
C. Thaiprayoon, W. Sudsutad, S. K. Ntouyas, Mixed nonlocal boundary value problem for implicit fractional integro-differential equations via $\psi$-Hilfer fractional derivative, <i>Adv. Differ. Equ.</i>, <b>2021</b> (2021), 1–24. 10.1186/s13662-020-03162-2
[28]
K. Deimling, <i>Nonlinear Functional Analysis</i>, Springer-Verlag, New York, 1985. 10.1007/978-3-662-00547-7
[29]
A. Granas, J. Dugundji, <i>Fixed Point Theory</i>, Springer-Verlag, New York, 2005.
Metrics
8
Citations
29
References
Details
Published
Jan 01, 2021
Vol/Issue
6(9)
Pages
9731-9756
Cite This Article
Weerawat Sudsutad, Sotiris K. Ntouyas, Chatthai Thaiprayoon (2021). Nonlocal coupled system for $ \psi $-Hilfer fractional order Langevin equations. AIMS Mathematics, 6(9), 9731-9756. https://doi.org/10.3934/math.2021566