On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals

Advances in Difference Equations

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[1] 0000 0001 0619 1117, grid.412125.1, Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;0000000109410645, grid.11794.3a, Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matematicas, University of Santiago de Compostela, Santiago de Compostela, Spain;

关键词: Multi-order fractional derivatives;    Impulse;    Caputo-type generalized fractional derivative;    Fractional integral;    Extremal solutions;    34A08;    34B10;    34B15;    34B37;   

DOI  :  10.1186/s13662-019-2183-4

来源: publisher

【 摘 要 】

In this paper, we present sufficient criteria ensuring the existence and uniqueness of solutions for nonlinear impulsive multi-order Caputo-type generalized fractional differential equations supplemented with nonlocal integro-initial value conditions involving generalized fractional integrals. Extremal solutions for the given problem are also discussed. The main tools of our study include Krasnoselskii’s fixed point theorem, Banach contraction mapping principle and monotone iterative technique. Examples are constructed for illustrating the obtained results.

【 授权许可】

CC BY