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A Sequential Nonlinear Random Fractional Differential Equation: Existence, Uniqueness and New Data Dependence
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  • Hafssa Yfrah,
  • Zoubir Dahmani,
  • Mehmet Zeki Sarikaya,
  • Farooq Ahmad
Hafssa Yfrah
University of Mostaganem
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Zoubir Dahmani
UMAB UNIVERSITY
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Mehmet Zeki Sarikaya
Duzce Universitesi
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Farooq Ahmad
Bahauddin Zakariya University, Multan, 60800, Pakistan
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Peer review status:UNDER REVIEW

18 May 2020Submitted to Mathematical Methods in the Applied Sciences
24 May 2020Assigned to Editor
24 May 2020Submission Checks Completed
24 May 2020Reviewer(s) Assigned

Abstract

In this work, we are concerned with a sequential nonlinear random differential equation of fractional order with nonlocal conditions. This is the first time in the literature where sequential problems and random ones are combined and considered. An existence and uniqueness of solutions for the problem is obtained by means of an appropriate random fixed point theorem. Then, new concepts on the sequential continuous and fractional derivative dependence are introduced. At the end, some results of stability on random, as well for deterministic, data dependence are discussed.