AIMS Mathematics

2019, Issue 3: 626-647. doi: 10.3934/math.2019.3.626
Research article Special Issues

Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions

• Received: 30 March 2019 Accepted: 29 May 2019 Published: 10 June 2019
• MSC : 26A33, 34A08, 34B15, 34A60

• In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modern tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented.

Citation: Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas. Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions[J]. AIMS Mathematics, 2019, 4(3): 626-647. doi: 10.3934/math.2019.3.626

Related Papers:

• In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modern tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented.

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