Abstract
Nowadays most researchers have been focused on fractional calculus because it has been proved that fractional derivatives could describe most phenomena better than usual derivations. Numerical parts of fractional calculus such as q-derivations are considered by researchers. In this work, our aim is to review the existence of solution for an m-dimensional system of fractional q-differential inclusions via sum of two multi-term functions under some boundary conditions on the time scale mathbb{T}_{t_{0}}= { t : t =t_{0}q^{n}}cup{0}, where ngeq1, t_{0} inmathbb{R}, and q in(0,1). By using the Banach contraction principle and some sufficient conditions, we guarantee the existence of solutions for the system of q-differential inclusions. Also, we provide an example, some algorithms, and a figure to illustrate our main result.
Highlights
The fractional calculus provides a meaningful generalization for the classical integration and differentiation to any order
The quantum calculus is equivalent to traditional infinitesimal calculus without the notion of limits
It is important that we increase our abilities by investigating complicate fractional differential equations and applications
Summary
The fractional calculus provides a meaningful generalization for the classical integration and differentiation to any order. R are continuous functions for i = 0, 1, 2, and Pcp(R) is the set of all compact subsets of Ntouyas et al studied the boundary value problem of first-order fractional differential equations given by cDβ0+1 [f1](x) = w1 x, f1(x), f2(x) , cDβ0+2 [f2](x) = w2 x, f1(x), f2(x) , t ∈ [0, 1]
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