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Full-Text Articles in Physical Sciences and Mathematics
Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer
Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer
Turkish Journal of Mathematics
Existence of a positive solution is shown for two singular two-point fractional boundary value problems with fractional boundary conditions using fixed point theory, lower order problems, and convolution of Green's functions. A nontrivial example is included.
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Turkish Journal of Mathematics
In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …