scholarly journals Boundary Value Problems Governed by Superdiffusion in the Right Angle: Existence and Regularity

2018 ◽  
Vol 2018 ◽  
pp. 1-29
Author(s):  
Ramzet Dzhafarov ◽  
Nataliya Vasylyeva
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Boundary Value ◽  
Boundary Problems ◽  
Classical Solvability ◽  
Hölder Classes ◽  
The Right ◽  
Holder Classes

For α∈(1,2), we analyze a stationary superdiffusion equation in the right angle in the unknown u=u(x1,x2): Dx1αu+Dx2αu=f(x1,x2), where Dxα is the Caputo fractional derivative. The classical solvability in the weighted fractional Hölder classes of the associated boundary problems is addressed.

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.

scholarly journals On solvability of some $ p $-Laplacian boundary value problems with Caputo fractional derivative

2021 ◽  
Vol 6 (12) ◽  
pp. 13622-13633
Author(s):  
Xiaoping Li ◽  
◽  
Dexin Chen ◽  
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Analysis Techniques

<abstract><p>The solvability of some $ p $-Laplace boundary value problems with Caputo fractional derivative are discussed. By using the fixed-point theory and analysis techniques, some existence results of one or three non-negative solutions are obtained. Two examples showed that the conditions used in this paper are somewhat easy to check.</p></abstract>

scholarly journals Impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Chanon Promsakon ◽  
Eakachai Suntonsinsoungvon ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Result ◽  
New Class ◽  
Nonlinear Alternative ◽  
Separated Boundary Conditions ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we study the existence and uniqueness for a new class of impulsive fractional boundary value problems with separated boundary conditions containing the Caputo fractional derivative of a function with respect to another function. The existence of solutions is established by using the Leray–Schauder nonlinear alternative, and the uniqueness result is proved via Banach’s contraction mapping principle. Some examples are also constructed to demonstrate the application of main results.

On a Legendre Tau method for fractional boundary value problems with a Caputo derivative

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Kazufumi Ito ◽  
Bangti Jin ◽  
Tomoya Takeuchi
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Boundary Value ◽  
Tau Method ◽  
Point Boundary ◽  
Leading Term ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we revisit a Legendre-tau method for two-point boundary value problems with a Caputo fractional derivative in the leading term, and establish an

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