Existence of solutions for a class of Caputo fractional \(q\)-difference inclusion on multifunctions by computational results. (English) Zbl 1524.39012
Summary: In this paper, we study a class of fractional \(q\)-differential inclusion of order \(0 < q <1\) under \(L^1\)-Caratheodory with convex-compact valued properties on multifunctions. By the use of existence of fixed point for closed valued contractive multifunction on a complete metric space which has been proved by H. Covitz and S. B. Nadler jun. [Isr. J. Math. 8, 5–11 (1970; Zbl 0192.59802)], we provide the existence of solutions for the inclusion problem via some conditions. Also, we give a couple of examples to elaborate our results and to present the obtained results by some numerical computations.
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 26A33 | Fractional derivatives and integrals |
Keywords:
existence of solution; fractional \(q\)-difference inclusion; integral boundary value problemCitations:
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