On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative

Hailong Ye and Rui Huang

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative D c0α2D c0α1yxp-2D c0α1yx=fx,yx, x > 0, y(0) = b0, D c0α1y(0)=b1, where D c0α1, D c0α2 are Caputo fractional derivatives, 0 1, and b0,b1∈R. Local existence of solutions is established by employing Schauder fixed point theorem. Then a growth condition imposed to f guarantees not only the global existence of solutions on the interval [0, +∞), but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to [0, +∞). Three illustrative examples are also presented. Existence results for initial value problems of ordinary differential equations with p‐Laplacian on the half‐axis follow as a special case of our results.

Date: 2015
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https://doi.org/10.1155/2015/174156

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:174156

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