scholarly journals Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
R. Leelavathi ◽  
G. Suresh Kumar ◽  
M. S. N. Murty ◽  
R. V. N. Srinivasa Rao
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Initial Value ◽  
Uniqueness Of Solutions

scholarly journals Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Jiang Zhu ◽  
Dongmei Liu
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Second Order ◽  
Dynamic Equations ◽  
Maximum Principles ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Approximation Theorems ◽  
Construction Techniques ◽  
Linear And Nonlinear

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

scholarly journals Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hojjat Afshari ◽  
Hossein Hosseinpour ◽  
H. R. Marasi
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Metric Spaces ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Contraction Mappings

AbstractIn this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete $\mathfrak{F}$ F -metric spaces for this purpose.

scholarly journals Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hojjat Afshari ◽  
H. R. Marasi ◽  
Jehad Alzabut
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Contraction Mappings ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Positive Functions

AbstractIn this paper, we consider initial value problems for two different classes of implicit ϕ-Hilfer fractional pantograph differential equations. We use different approach that is based on $\alpha -\psi $ α − ψ -contraction mappings to demonstrate the existence and uniqueness of solutions for the proposed problems. The mappings are defined in appropriate cones of positive functions. The presented examples demonstrate the efficiency of the used method and the consistency of the proposed results.

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