Dynamics and Stability Results for Nonlinear Neutral Pantograph Equations via Hilfer-Hadamard Fractional Derivative

2019 ◽  
Vol 8 (1) ◽  
pp. 39-50
Author(s):  
D. Vivek ◽  
K. Kanagarajan ◽  
S. Harikrishnan
Keyword(s):  
Fractional Derivative ◽  
Hadamard Fractional Derivative ◽  
Stability Results

scholarly journals A study of fractional integro-differential equations via Hilfer-Hadamard fractional derivative

2019 ◽  
Vol 27 (1) ◽  
pp. 71-84
Author(s):  
D. Vivek ◽  
K. Kanagarajan ◽  
E. M. Elsayed
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Of Solution ◽  
Ulam Stability ◽  
Hadamard Fractional Derivative ◽  
Stability Results

Abstract In this paper, we investigate the existence of solution of integro-differential equations (IDEs) with Hilfer-Hadamard fractional derivative. The main results are obtained by using Schaefer’s fixed point theorem. Some Ulam stability results are presented.

scholarly journals On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
M. D. Qassim ◽  
K. M. Furati ◽  
N.-E. Tatar
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Global Solution ◽  
Differential Inequality ◽  
Source Term ◽  
Existence Of Solutions ◽  
Hadamard Fractional Derivative ◽  
Fractional Differential

This paper studies a fractional differential inequality involving a new fractional derivative (Hilfer-Hadamard type) with a polynomial source term. We obtain an exponent for which there does not exist any global solution for the problem. We also provide an example to show the existence of solutions in a wider space for some exponents.

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 Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Ahmed Salem ◽  
Noorah Mshary ◽  
Moustafa El-Shahed ◽  
Faris Alzahrani
Keyword(s):  
Fractional Derivative ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Hadamard Fractional Derivative ◽  
Compact Case ◽  
New Type ◽  
Sturm Liouville ◽  
Hadamard Fractional Integral

In this work, through using the Caputo–Hadamard fractional derivative operator with three nonlocal Hadamard fractional integral boundary conditions, a new type of the fractional-order Sturm–Liouville and Langevin problem is introduced. The existence of solutions for this nonlinear boundary value problem is theoretically investigated based on the Krasnoselskii in the compact case and Darbo fixed point theorems in the noncompact case with aiding the Kuratowski’s measure of noncompactness. To demonstrate the applicability and validity of the main gained findings, some numerical examples are included.

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