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Dhage iterative principle for quadratic perturbation of fractional boundary value problems with finite delay
Author(s) -
Gupta Vidushi,
Bora Swaroop Nandan,
Nieto Juan J.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5643
Subject(s) - mathematics , lipschitz continuity , uniqueness , fixed point theorem , quadratic equation , banach space , boundary value problem , picard–lindelöf theorem , mathematical analysis , nonlinear system , fixed point , sequence (biology) , physics , geometry , quantum mechanics , biology , genetics
In this article, by employing Dhage iterative method embodied in current hybrid fixed point theorem (HFPT) of Dhage, we derive an algorithm for the numerical solutions via construction of a sequence of successive approximations for a fractional order boundary value problem (FBVP) with finite delay. By using this technique, we obtain existence as well as approximation of solutions under weaker partial Lipschitz and partial compactness type conditions in a partially ordered Banach space. Additionally, we prove an existence and uniqueness theorem under a weaker partial nonlinear Lipschitz condition. The assumptions and main outcomes are also illustrated by two examples.