Abstract
We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.
Highlights
By means of different tools from nonlinear analysis, many classes of differential equations with Caputo fractional derivative have extensively been studied in books [1,2,3,4,5] and in some papers, for example, [6,7,8,9,10,11]
We consider a new fractional derivative which interpolates the Hilfer, Hilfer–Hadamard, Riemann–Liouville, Hadamard, Caputo, Caputo–Hadamard, generalized and Caputo-type fractional derivatives, as well as the Weyl and Liouville fractional derivatives for particular cases of integration extremes. for more details, see [14,15,16,17,18,19,20,21] and the references therein. It is well known [22] that the comparison principle for initial value problems of ordinary differential equations is a very useful tool in the study of qualitative and quantitative theory
Motivated by the works above, we establish in this paper existence and uniqueness results to the terminal value problem of the following Hilfer–Katugampola type fractional differential equation: ρ
Summary
By means of different tools from nonlinear analysis, many classes of differential equations with Caputo fractional derivative have extensively been studied in books [1,2,3,4,5] and in some papers, for example, [6,7,8,9,10,11]. For more details, see [14,15,16,17,18,19,20,21] and the references therein It is well known [22] that the comparison principle for initial value problems of ordinary differential equations is a very useful tool in the study of qualitative and quantitative theory. Motivated by the works above, we establish in this paper existence and uniqueness results to the terminal value problem of the following Hilfer–Katugampola type fractional differential equation: ρ α,β α,β. No papers on terminal value problem for implicit fractional differential equations exist in the literature, in particular for those involving the Hilfer–Katugampola fractional derivative.
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