High‐order convergent methods for singularly perturbed quasilinear problems with integral boundary conditions

2020 ◽  
Author(s):  
Sunil Kumar ◽  
Shashikant Kumar ◽  
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
High Order ◽  
Singularly Perturbed ◽  
Integral Boundary ◽  
Quasilinear Problems

scholarly journals Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

scholarly journals Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 130
Author(s):  
Suphawat Asawasamrit ◽  
Yasintorn Thadang ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Nonlinear Alternative

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

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