scholarly journals Existence Results for ψ -Hilfer Fractional Integro-Differential Hybrid Boundary Value Problems for Differential Equations and Inclusions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Chanakarn Kiataramkul ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Research Work ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Results ◽  
New Class ◽  
Multivalued Operators ◽  
Differential Equations And Inclusions

In this research work, we study a new class of ψ -Hilfer hybrid fractional integro-differential boundary value problems with nonlocal boundary conditions. Existence results are established for single and multivalued cases, by using suitable fixed-point theorems for the product of two single or multivalued operators. Examples illustrating the main results are also constructed.

scholarly journals A Survey on Existence Results for Boundary Value Problems of Hilfer Fractional Differential Equations and Inclusions

Foundations ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 63-98 ◽  
Author(s):  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Results ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.

scholarly journals Existence Results for Nonlocal Multi-Point and Multi-Term Fractional Order Boundary Value Problems

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 70 ◽  
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
New Class ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and integral boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We also demonstrate the application of the obtained results with the aid of examples.

scholarly journals Existence theory for nonlocal boundary value problems involving mixed fractional derivatives

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Bashir Ahmad ◽  
K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Theory ◽  
Nonlinear Alternative ◽  
Mixed Fractional Derivatives ◽  
Differential Equations And Inclusions

In this paper, we develop the existence theory for a new kind of nonlocal three-point boundary value problems for differential equations and inclusions involving both left Caputo and right Riemann–Liouville fractional derivatives. The Banach and Krasnoselskii fixed point theorems and the Leray–Schauder nonlinear alternative are used to obtain the desired results for the singlevalued problem. The existence of solutions for the multivalued problem concerning the upper semicontinuous and Lipschitz cases is proved by applying nonlinear alternative for Kakutani maps and Covitz and Nadler fixed point theorem. Examples illustrating the main results are also presented.

Initial-boundary value problems for a time-fractional differential equation with involution perturbation

2019 ◽  
Vol 14 (3) ◽  
pp. 312 ◽  
Author(s):  
Nasser Al-Salti ◽  
Sebti Kerbal ◽  
Mokhtar Kirane
Keyword(s):  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Nonlocal Boundary Conditions ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value ◽  
Formal Solutions ◽  
The Given

Direct and inverse initial-boundary value problems of a time-fractional heat equation with involution perturbation are considered using both local and nonlocal boundary conditions. Results on existence of formal solutions to these problems are presented. Solutions are expressed in a form of series expansions using appropriate orthogonal basis obtained by separation of variables. Convergence of series solutions are obtained by imposing certain conditions on the given data. Uniqueness of the obtained solutions are also discussed. The obtained general solutions are illustrated by an example using an appropriate choice of the given data.

Existence results for a second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 53 (1) ◽  
pp. 42-52
Author(s):  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems , where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞f(t, λ a) exists uniformly in a ∈ Sk−1, we have shown that the problem has at least one solution.

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