Abstract
In the present research manuscript, we formulate a new generalized structure of the nonlinear Caputo fractional quantum multi-integro-differential equation in which such a multi-order structure of quantum integrals is considered for the first time. In fact, in the light of this type of boundary value problem equipped with the multi-integro-differential setting, one can simply study different cases of the existing usual integro-differential problems in the literature. In this direction, we utilize well-known analytical techniques to derive desired criteria which guarantee the existence of solutions for the proposed multi-order quantum multi-integro-differential problem. Further, some numerical examples are considered to examine our theoretical and analytical findings using the proposed methods.
Highlights
As years and even decades go by, the human beings need to be acquainted with different natural phenomena more and more
Lemma 3.1, it is natural that the fixed point of A is considered as a solution for the nonlinear Caputo fractional quantum multi-integro-differential problem (1)
Theorem 2.2 implies that the given nonlinear Caputo fractional quantum multi-integro-differential problem (1) has at least one solution on the interval [0, 1], and so this completes the proof
Summary
As years and even decades go by, the human beings need to be acquainted with different natural phenomena more and more. In the light of Lemma 3.1 and in relation to the proposed nonlinear Caputo fractional quantum multi-integro-differential equation (1), we construct an operator A : W → W as follows: We are in the position to derive required existence criteria for the given nonlinear Caputo fractional quantum multi-integro-differential problem (1).
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