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Well‐posedness and iterative formula for fractional oscillator equations with delays
Author(s) -
Pang Denghao,
Jiang Wei,
Liu Song,
Niazi Azmat Ullah Khan
Publication year - 2019
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.5572
Subject(s) - mathematics , iterative method , fractional calculus , function (biology) , mittag leffler function , mathematical analysis , mathematical optimization , evolutionary biology , biology
This paper investigates the well‐posedness and iterative formula for fractional oscillator equations with two different fractional orders and time delays. By the mathematical induction, a new generalized Grönwall's inequality in terms of a multivariate Mittag‐Leffler function is derived with an iteration argument. Subsequently, using the inequality, a generalized Mittag‐Leffler estimation of the solution is proposed. Furthermore, the explicit solution and iterative formula, as well as the unique existence, are presented on the basis of the method of steps. Finally, an example is given to illustrate the validity of our main results.