Existence and stability results for Langevin equations with Hilfer fractional derivative

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
S. Harikrishnan ◽  
K. Kanagarajan ◽  
E. M. Elsayed
Keyword(s):  
Fractional Derivative ◽  
Langevin Equations ◽  
Hilfer Fractional Derivative ◽  
Existence And Stability ◽  
Stability Results

scholarly journals Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 94 ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Hilfer Fractional Derivative ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Stability Results

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

scholarly journals Nonlocal boundary value problems for integro-differential Langevin equation via the generalized Caputo proportional fractional derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bounmy Khaminsou ◽  
Chatthai Thaiprayoon ◽  
Jehad Alzabut ◽  
Weerawat Sudsutad
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Langevin Equation ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Langevin Equations ◽  
Paper Study ◽  
Integral Conditions ◽  
Existence And Stability

AbstractResults reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions. The main theorems are proved with the help of Banach’s, Krasnoselskii’s, and Schaefer’s fixed point theorems and Ulam’s approach. Finally, an example is given to demonstrate the applicability of our theoretical findings.

Ulam stability for Hilfer type fractional differential inclusions via the weakly Picard operators theory

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Adrian Petruşel
Keyword(s):  
Fractional Derivative ◽  
Operator Theory ◽  
Differential Inclusions ◽  
Ulam Stability ◽  
Hilfer Fractional Derivative ◽  
Picard Operator ◽  
Fractional Differential ◽  
Differential Equations And Inclusions ◽  
Weakly Picard Operator ◽  
Stability Results

AbstractConsiderable attention has been recently given to the existence of solutions of initial or boundary value problems for fractional differential equations and inclusions with Hilfer fractional derivative. Motivated by these results, in this paper we will present existence, data dependence and Ulam stability results for some differential inclusions with Hilfer fractional derivative. The results follow as applications of the multi-valued weakly Picard operator theory. An example illustrates the main result of the paper.

scholarly journals Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 1-19
Author(s):  
Mohammed A. Almalahi ◽  
Satish. K Panchal
Keyword(s):  
Differential Equation ◽  
Hilfer Fractional Derivative ◽  
Implicit Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Existence And Stability ◽  
Fractional Differential ◽  
The Stability ◽  
Fixed Point Techniques ◽  
Stability Results

In this paper, we study the class of boundary value problems for a nonlinear implicit fractional differential equation with periodic conditions involving a ψ-Hilfer fractional derivative. With the help of properties Mittag-Leffler functions, and fixed-point techniques, we establish the existence and uniqueness results, whereas the generalized Gronwall inequality is applied to get the stability results. Also, an example is provided to illustrate the obtained results.  

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