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On using coupled fixed‐point theorems for mild solutions to coupled system of multipoint boundary value problems of nonlinear fractional hybrid pantograph differential equations
Author(s) -
Iqbal Muhammad,
Shah Kamal,
Khan Rahmat Ali
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5799
Subject(s) - pantograph , mathematics , nonlinear system , boundary value problem , mathematical analysis , fixed point theorem , differential equation , type (biology) , class (philosophy) , delay differential equation , computer science , physics , mechanical engineering , ecology , quantum mechanics , artificial intelligence , engineering , biology
The aims of this manuscript is to establish conditions for obtaining mild solutions to a coupled systems of multipoint boundary value problems (BVPs) of fractional order hybrid differential equations (FHDEs) with nonlinear perturbations of second type. In the concerned problem, we consider a proportional type delay that represent a famous class of differential equation called pantograph equations. Hence, we establish sufficient conditions for at least one mild solution to the coupled system of fractional hybrid pantograph differential equations (FHPDEs) by using Burton and couple‐type fixed‐point theorems. We also provide examples to show the applicability of our results.