A novel fractional structure of a multi-order quantum multi-integro-differential problem

• Main Authors: Nguyen Duc Phuong, Fethiye Muge Sakar, Sina Etemad, Shahram Rezapour
• Format: Article
• Language: English
• Published: SpringerOpen 2020-11-01
• Series: Advances in Difference Equations
• Subjects: Boundary value problem; Multi-integro-differential equation; Quantum calculus; The Caputo quantum derivative
• Online Access: http://link.springer.com/article/10.1186/s13662-020-03092-z

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.