Existence of solutions for a system of singular sum fractional q-differential equations via quantum calculus

Abstract

In this study, we discuss the existence of positive solutions for the system of m-singular sum fractional q-differential equationsq-derivative of order α, here q ∈ (0, 1), function g i is of Carathéodory type, h i satisfy the Lipschitz condition and g i (t, x 1 , . . . , x 2m ) is singular at t = 0, for 1 ≤ i ≤ m. By means of Krasnoselskii's fixed point theorem, the Arzelà-Ascoli theorem, Lebesgue dominated theorem and some norms, the existence of positive solutions is obtained. Also, we give an example to illustrate the primary effects.MSC: Primary 34A08; 39A12; secondary 34B16

A coupled system of q-fractional Lane-Emden problem involving three sequential q-fractional derivatives with stability inequality

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A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

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