Existence of solutions for multi-point boundary value problem of fractional q-difference equation
نویسندگان
چکیده
Fractional differential calculus have recently been addressed by many researchers of various fields of science and engineering such as physics, chemistry, biology, economics, control theory, and biophysics, etc. [1-4]. In particular, the existence of solutions to fractional boundary value problems is under strong research recently, see [5-7] and references therein. The fractional q-difference calculus had its origin in the works by Al-Salam [8] and Agarwal [9]. More recently, perhaps due to the explosion in research within the fractional differential calculus setting, new developments in this theory of fractional q-difference calculus were made, specifically, q-analogues of the integral and differential fractional operators properties such as the q-Laplace transform, q-Taylor’s formula [10,11], just to mention some. The question of the existence of solutions for fractional q-difference boundary value problems is in its infancy, being few results available in the literature. Ferreira [12] considered the existence of positive solutions to nonlinear q-difference boundary value problem: (D q u)(t) = −f(t, u(t)), 0 < t < 1, 1 < α ≤ 2 u(0) = u(1) = 0.
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