A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

Advances in Difference Equations

Francisco Martinez¹  Eva Kaslik²  Sina Etemad³  Shahram Rezapour⁴  Mohammed K. A. Kaabar⁵  Abdelkader Amara⁶  Ahmed Nouara⁶ 

[1] Department of Applied Mathematics and Statistics, Technological University of Cartagena, 30203, Cartagena, Spain;Department of Mathematics and Computer Science, West University of Timisoara, 300223, Timisoara, Romania;Institute e-Austria Timisoara, Bd. V. Parvan nr. 4, 300223, Timisoara, Romania;Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia;Jabalia Camp, United Nations Relief and Works Agency (UNRWA) Palestinian Refugee Camp, Gaza Strip Jabalya, State of Palestine;Laboratory of Applied Mathematics, University of Kasdi Merbah, 30000, Ouargla, Algeria;

关键词: Hybrid boundary problem;    Riemann–Liouville derivative;    Dhage’s technique;    Stability;    34A08;    34A12;   

DOI  :  10.1186/s13662-021-03502-w

来源: Springer

【 摘 要 】

In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

【 授权许可】

CC BY