Some properties of implicit impulsive coupled system via φ-Hilfer fractional operator

Boundary value problems

Satish K. Panchal¹  Mohammed A. Almalahi² 

[1] Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, 431001, Aurangabad, (M.S), India;Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, 431001, Aurangabad, (M.S), India;Department of Mathematics, Hajjah University, Hajjah, Yemen;

关键词: φ;    Terminal conditions;    Impulsive coupled system;    Existence theory;    Fixed point theorem;    34A08;    34B15;    34A12;    47H10;   

DOI  :  10.1186/s13661-021-01543-4

来源: Springer

【 摘 要 】

The major goal of this work is investigating sufficient conditions for the existence and uniqueness of solutions for implicit impulsive coupled system of φ-Hilfer fractional differential equations (FDEs) with instantaneous impulses and terminal conditions. First, we derive equivalent fractional integral equations of the proposed system. Next, by employing some standard fixed point theorems such as Leray–Schauder alternative and Banach, we obtain the existence and uniqueness of solutions. Further, by mathematical analysis technique we investigate the Ulam–Hyers (UH) and generalized UH (GUH) stability of solutions. Finally, we provide a pertinent example to corroborate the results obtained.

【 授权许可】

CC BY