Results 1 to 10 of about 163 (105)

On Solutions of Hybrid–Sturm‐Liouville–Langevin Equations with Generalized Versions of Caputo Fractional Derivatives

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The main intention of this research article is to introduce a new class of generalized fractional differential equations that fall into the categories of Sturm‐Liouville’s, Langevin’s, and hybrid’s problems involving Y‐Caputo fractional derivatives.
Abdellatif Boutiara, Hanan A. Wahash, Heba Y. Zahran, Emad E. Mahmoud, Abdel-Haleem Abdel-Aty, El Sayed Yousef, Yusuf Gurefe   +6 more
wiley   +3 more sources

Solvability of Implicit Fractional Order Integral Equation in ℓp(1 ≤ p<∞) Space via Generalized Darbo’s Fixed Point Theorem

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
We present a generalization of Darbo’s fixed point theorem in this article, and we use it to investigate the solvability of an infinite system of fractional order integral equations in ℓp(1 ≤ p<∞) space. The fundamental tool in the presentation of our proofs is the measure of noncompactness (mnc) approach.
Inzamamul Haque, Javid Ali, M. Mursaleen, Reny George   +3 more
wiley   +3 more sources

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
In this article, we study the existence of the solution for the fractional differential equations of sequential type with nonlocal integral boundary conditions. The main results are established with the aid of Darbo’s fixed point theorem and Hausdorff’s measure of noncompactness method.
Muath Awadalla, Kinda Abuasbeh, Murugesan Manigandan, Ahmed A. Al Ghafli, Hassan J. Al Salman, Yusuf Gurefe   +5 more
wiley   +3 more sources

Existence and Uniqueness of Solutions for a Third‐Order Three‐Point Boundary Value Problem via Measure of Noncompactness

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this paper, we consider a nonlinear third‐order three‐point boundary value problem and give the existence and uniqueness of solutions by constructing Green’s function and using its properties. The methods used here are based on Darbo’s fixed point theorem combined with the technique of measure of noncompactness.
Chen Yang, Guotao Wang
wiley   +2 more sources

On System of Mixed Fractional Hybrid Differential Equations

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this article, we find the necessary conditions for the existence and uniqueness of solutions to a system of hybrid equations that contain mixed fractional derivatives (Caputo and Riemann‐Liouville). We also verify the stability of these solutions using the Ulam‐Hyers (U‐H) technique.
Muath Awadalla, Nazim I. Mahmudov, Hüseyin Işık   +2 more
wiley   +1 more source

Darbo Fixed Point Criterion on Solutions of a Hadamard Nonlinear Variable Order Problem and Ulam‐Hyers‐Rassias Stability

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results are obtained via generalized intervals and piecewise constant functions and the relevant Green function, by converting the existing Hadamard variable order fractional boundary ...
Shahram Rezapour, Zoubida Bouazza, Mohammed Said Souid, Sina Etemad, Mohammed K. A. Kaabar, Tianqing An   +5 more
wiley   +1 more source

Existence of Solutions for Nonlinear Integral Equations in Tempered Sequence Spaces via Generalized Darbo‐Type Theorem

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
Two concepts—one of Darbo‐type theorem and the other of Banach sequence spaces—play a very important and active role in ongoing research on existence problems. We first demonstrate the generalized Darbo‐type fixed point theorems involving the concept of continuous functions.
S. A. Mohiuddine, Anupam Das, Abdullah Alotaibi, Santosh Kumar   +3 more
wiley   +1 more source

Investigation of the Generalized Proportional Langevin and Sturm–Liouville Fractional Differential Equations via Variable Coefficients and Antiperiodic Boundary Conditions with a Control Theory Application Arising from Complex Networks

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
This article studies the existence theory of an innovation type of generalized proportional fractional differential equations with the assistance of the technique of Kuratowski measure on noncompactness combined with the fixed‐point theorem of Mönch.
Abdellatif Boutiara, Mohammed K. A. Kaabar, Zailan Siri, Mohammad Esmael Samei, Xiao-Guang Yue, Abdellatif Ben Makhlouf   +5 more
wiley   +1 more source

Solution of a Fractional Integral Equation Using the Darbo Fixed Point Theorem

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
The concept of measure of noncompactness in a Banach space is used in this paper to extend some tripled fixed point theorems. We prove the existence of fractional integral equation solutions using a generalized Darbo fixed point theorem. To demonstrate the validity of the main result, an example is provided.
Bhuban Chandra Deuri, Marija V. Paunović, Anupam Das, Vahid Parvaneh, Ali Jaballah   +4 more
wiley   +1 more source

A Study on ψ‐Caputo‐Type Hybrid Multifractional Differential Equations with Hybrid Boundary Conditions

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this research paper, we investigate the existence, uniqueness, and Ulam–Hyers stability of hybrid sequential fractional differential equations with multiple fractional derivatives of ψ‐Caputo with different orders. Using an advantageous generalization of Krasnoselskii’s fixed point theorem, we establish results of at least one solution, whereas the ...
Fouad Fredj, Hadda Hammouche, Mohammed S. Abdo, Wedad Albalawi, Abdulrazak H. Almaliki, Melike Kaplan   +5 more
wiley   +1 more source