Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay
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DOI: 10.1007/s00009-018-1258-x
Abstract: In this paper, we investigate an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. More precisely, observing $$\nu (t-k)^{\overline{\nu -1}}\le {t^{\bar{\nu }}}$$ν(t-k)ν-1¯≤tν¯, we… read more here.
Keywords: fractional difference; difference system; nabla fractional; nonlinear nabla ... See more keywords
Gronwall's inequality for a nabla fractional difference system with a retarded argument and an application
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DOI: 10.1080/10236198.2019.1581180
Abstract: ABSTRACT We study the nabla fractional difference system with retarded argument. There are two major ingredients. A Gronwall's inequality for the nabla case is given. This allows us to evaluate the solution of nabla fractional… read more here.
Keywords: difference system; difference; fractional difference; nabla fractional ... See more keywords
Ulam-Hyers stability results for a novel nonlinear Nabla Caputo fractional variable-order difference system
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DOI: 10.3906/mat-2008-53
Abstract: This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variableorder and fixed initial valuable. By applying Krasnoselskii’s fixed point theorem, we give some sufficient conditions to guarantee the existence… read more here.
Keywords: difference system; nonlinear nabla; nabla caputo; hyers stability ... See more keywords