New existence criteria of the solutions for a variational relation problem

Optimization ◽  
2017 ◽  
Vol 66 (5) ◽  
pp. 675-689 ◽  
Author(s):  
Mircea Balaj
Keyword(s):  
Variational Relation Problem ◽  
Existence Criteria

scholarly journals On a new structure of the pantograph inclusion problem in the Caputo conformable setting

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sabri T. M. Thabet ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Differential Equation ◽  
Inclusion Problem ◽  
Integral Conditions ◽  
Lower Semi ◽  
First Time ◽  
Existence Criteria

Abstract In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding to the inclusion version of the three-point Caputo conformable pantograph BVP subject to Riemann–Liouville conformable integral conditions. To achieve this aim, we establish our main results in some cases including the lower semi-continuous, the upper semi-continuous and the Lipschitz set-valued maps. Eventually, the last part of the present research is devoted to proposing two numerical simulative examples to confirm the consistency of our findings.

scholarly journals An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Sh. Rezapour ◽  
B. Azzaoui ◽  
B. Tellab ◽  
S. Etemad ◽  
H. P. Masiha
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Caputo Fractional Derivatives ◽  
Control Functions ◽  
Existence Of Positive Solutions ◽  
Semilinear Differential Equation ◽  
The Given ◽  
Existence Criteria

In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

scholarly journals Hyers-Ulam Stability and Existence Criteria for the Solution of Second-Order Fuzzy Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Noor Jamal ◽  
Muhammad Sarwar ◽  
M. Motawi Khashan
Keyword(s):  
Differential Equations ◽  
Physical Model ◽  
Unique Solution ◽  
Second Order ◽  
Ulam Stability ◽  
Existence Criteria ◽  
Sumudu Transforms

In this paper, existence, uniqueness, and Hyers-Ulam stability for the solution of second-order fuzzy differential equations (FDEs) are studied. To deal a physical model, it is required to insure whether unique solution of the model exists. The natural transform has the speciality to converge to both Laplace and Sumudu transforms only by changing the variables. Therefore, this method plays the rule of checker on the Laplace and Sumudu transforms. We use natural transform to obtain the solution of the proposed FDEs. As applications of the established results, some nontrivial examples are provided to show the authenticity of the presented work.

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