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Solutions of sum‐type singular fractional q integro‐differential equation with m ‐point boundary value problem using quantum calculus
Author(s) -
Ahmadian Ali,
Rezapour Shahram,
Salahshour Soheil,
Samei Mohammad Esmael
Publication year - 2020
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.6591
Subject(s) - mathematics , fractional calculus , boundary value problem , fixed point theorem , mathematical analysis , type (biology) , differential equation , biology , ecology
Nowadays, many researchers have considerable attention to fractional calculus as a useful tool for modeling of different phenomena in the world. In this work, we investigate the sum‐type singular nonlinear fractional q integro‐differential equations with m ‐point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo q derivative, Riemann–Liouville fractional q integral, and a fixed point theorem on a real Banach space X , which has a partial order by using a cone P ⊂ X . The proofs are based on solving the operators equation. By providing seven algorithms, four tables, and three figures, we give two numerical examples to illustrate our main result.