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Balance function is one of the joint factors to determine fall in risk theory. It helps to moderate the progression and riskiness of falls for detecting balance and fall risk factors. Nevertheless, the objective measures for balance function require expensive equipment with the assessment of any expertise. We establish the existence and uniqueness of a multi-order fractional differential equations based on $\psi$- Hilfer operator on time scales with balance function. This class describes the dynamic of time scales derivative. Our tool is based on the Schauder fixed point theorem. Here, sufficient conditions for Ulam-stability are given.
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참고문헌 (17)
참고문헌 신청
R.P. Agarwal / 1999 / Basic calculus on time scales and some of its applications / Results Math. 35:3~22
A. Ahmadkhanlu / 2012 / On the existence and uniqueness of solu-tion of initial value problem for fractional order differential equations on time scales / B. Iran. Math. Soc 38:241~252
N. Benkhettou / 2016 / Existence and uniqueness of solution for a fractional Riemann-lioville initial value problem on time scales / Journal of King Saud University-Science 28:87~92
M. Bohner / 2003 / Advances in Dynamic Equations on Time Scales / Birkhauser
M. Bohner / Dtnamica equations on times scale / Birkhauser
A. Ahmadkhanlu / 2012 / On the existence and uniqueness of solu-tion of initial value problem for fractional order differential equations on time scales / B. Iran. Math. Soc 38:241~252
N. Benkhettou / 2016 / Existence and uniqueness of solution for a fractional Riemann-lioville initial value problem on time scales / Journal of King Saud University-Science 28:87~92
M. Bohner / 2003 / Advances in Dynamic Equations on Time Scales / Birkhauser
M. Bohner / Dtnamica equations on times scale / Birkhauser
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