The exponential matrix function and linear differential equations

1977 ◽  
Vol 8 (1) ◽  
pp. 117-119
Author(s):  
J. ASTIN
Keyword(s):  
Differential Equations ◽  
Matrix Function ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Exponential Matrix

scholarly journals Existence and Stability Results on Hadamard Type Fractional Time-Delay Semilinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1242
Author(s):  
Nazim Mahmudov ◽  
Areen Al-Khateeb
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Explicit Form ◽  
Nonlinear Equations ◽  
Matrix Function ◽  
Linear Differential Equations ◽  
Existence And Stability ◽  
Linear Differential ◽  
Stability Results

A delayed perturbation of the Mittag-Leffler type matrix function with logarithm is proposed. This combines the classic Mittag–Leffler type matrix function with a logarithm and delayed Mittag–Leffler type matrix function. With the help of this introduced delayed perturbation of the Mittag–Leffler type matrix function with a logarithm, we provide an explicit form for solutions to non-homogeneous Hadamard-type fractional time-delay linear differential equations. We also examine the existence, uniqueness, and Ulam–Hyers stability of Hadamard-type fractional time-delay nonlinear equations.

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