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A framework of linear canonical transform on pseudo‐differential operators and its application
Author(s) -
Kumar Manish,
Pradhan Tusharakanta
Publication year - 2021
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.7501
Subject(s) - mathematics , fourier integral operator , canonical form , boundary value problem , class (philosophy) , mathematical analysis , representation (politics) , partial differential equation , operator theory , composition (language) , differential equation , pure mathematics , linguistics , philosophy , artificial intelligence , politics , computer science , law , political science
The primary aim of this paper is to define a class of pseudo‐differential operators (PDOs) involving linear canonical transform (LCT) associated with the symbol b ( x , y ). An integral representation of PDOsP b α , β , γ , δis given. Boundedness of the composition of operatorsΔ x , α , β kandP b α , β , γ , δare derived. Further, new integral operatorsP b α , β , γ , δare defined, and their boundedness properties are also investigated. The secondary aim is to find some applications of LCT to solve the boundary value problems of generalized partial differential equations and obtain their solution in closed form. Furthermore, particular cases of these differential equations are discussed, and demonstration of these equations' solutions are shown graphically.