Comparison principles for differential equations involving Caputo fractional derivative with Mittag-Leffler non-singular kernel

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dc.contributor.authorAl-Refai, Mohammed
dc.date.accessioned2022-01-05T19:48:43Z
dc.date.available2022-01-05T19:48:43Z
dc.date.issued2018-01-29
dc.description.abstractIn this article we study linear and nonlinear differential equations involving the Caputo fractional derivative with Mittag-Leffler non-singular kernel of order 0 < α < 1. We first obtain a new estimate of the fractional derivative of a function at its extreme points and derive a necessary condition for the existence of a solution to the linear fractional equation. The condition obtained determines the initial condition of the associated fractional initial-value problem. Then we derive comparison principles for the linear fractional equations, and apply these principles for obtaining norm estimates of solutions and to obtain a uniqueness results. We also derive lower and upper bounds of solutions. The applicability of the new results is illustrated through several examples.
dc.description.departmentMathematics
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationAl-Refai, M. (2018). Comparison principles for differential equations involving Caputo fractional derivative with Mittag-Leffler non-singular kernel. <i>Electronic Journal of Differential Equations, 2018</i>(36), pp. 1-10.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15092
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFractional differential equations
dc.subjectMaximum principle
dc.titleComparison principles for differential equations involving Caputo fractional derivative with Mittag-Leffler non-singular kernel
dc.typeArticle

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