Comparison principles for differential equations involving Caputo fractional derivative with Mittag-Leffler non-singular kernel
Date
2018-01-29
Authors
Al-Refai, Mohammed
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Fractional differential equations, Maximum principle
Citation
Al-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.
Rights
Attribution 4.0 International