97 research outputs found
Some Existence Results for a System of Nonlinear Sequential Fractional Differential Equations with Coupled Nonseparated Boundary Conditions
No full textThis article concerns with the existence and uniqueness theory of solutions for sequential fractional differential system involving Caputo fractional derivatives of order 1<alpha, beta<2 with coupled nonseparated boundary conditions. The standard tools of the fixed point theory were used to establish the main results. Application is introduced to show the validity of our results
Applicability of Mönch’s Fixed Point Theorem on Existence of a Solution to a System of Mixed Sequential Fractional Differential Equation
No full textIn this paper, we study the existence and uniqueness of the solution for a coupled system of mixed fractional differential equations. The main results are established with the aid of “Mönch’s fixed point theorem.” In addition, an applied example that supports the theoretical results reached through this study is included
Fractional Hermite Functions: Power Series Solutions, Rodrigues Representation, and Orthogonality Properties
No full text T his paper develops a rigorous framework for fractional Hermite func tions using Caputo derivatives. We establish three fundamental contribu tions. First, we derive a complete power series solution to the fractional Hermite equation expressed through the basis {xkα}∞ k=0 , proving absolute convergence for all x ∈ C through careful asymptotic analysis of the coefficients. Second, we introduce and characterize both even and odd fractional Hermite functions H(α) n (x), deriving their explicit representa tions, recurrence relations, and a fractional Rodrigues-type formula that generalizes the classical case. Third, we demonstrate their orthogonality properties under the weight function wα(x) = |x|α−1e−|x|2α, obtaining exact normalization constants. The theoretical results are supported by comprehensive graphical analysis showing the systematic deformation of classical Hermite polynomial features as α varies. These developments provide new tools for fractional spectral methods and advance the under standing of orthogonal function systems in fractional calculus
On the Controllability of Conformable Fractional Deterministic Control Systems in Finite Dimensional Spaces
No full textIn this paper, we establish a set of convenient conditions of controllability for semilinear fractional finite dimensional control systems involving conformable fractional derivative. Indeed, sufficient conditions of controllability for a semilinear conformable fractional system are presented, assuming that the corresponding linear systems are controllable. The present method is based on conformable fractional exponential matrix, Gramian matrix, and the iterative technique. Two illustrated examples are carried out to establish the facility and efficiency of this technique
Existence Results for Caputo Tripled Fractional Differential Inclusions with Integral and Multi-Point Boundary Conditions
No full textIn this study, based on Coitz and Nadler’s fixed point theorem and the non-linear alternative for Kakutani maps, existence results for a tripled system of sequential fractional differential inclusions (SFDIs) with integral and multi-point boundary conditions (BCs) in investigated. A practical examples are given to illustrate the obtained the theoretical results
On System of Mixed Fractional Hybrid Differential Equations
No full textIn 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. Finally, this study ends with applied examples that show how to proceed and verify the conditions of our theoretical results
Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods
No full textThis paper presents an investigation into original analytical solutions of the (2+1)-dimensional combined potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations. For this purpose, the generalized Kudryashov technique (GKT) and exponential rational function technique (ERFT) have been applied to deal with the equation. These two methods have been applied to the model for the first time, and the the generalized Kudryashov method has an important place in the literature. The characteristics of solitons are unveiled through the use of three-dimensional, two-dimensional, contour, and density plots. Furthermore, we conducted a stability analysis on the acquired results. The results obtained in the article were seen to be different compared to other results in the literature and have not been published anywhere before
Existence and Stability of Ulam–Hyers and Generalized Ulam–Hyers for the Generalized Langevin–Sturm–Liouville Equation Involving Generalized Liouville–Caputo Type
No full textThis paper focuses on investigating the existence, uniqueness, and stability of Ulam–Hyers (U-H) and generalized Ulam–Hyers (G-U-H) solutions for the generalized Langevin–Sturm–Liouville equation, which involves generalized Liouville–Caputo derivatives and antiperiodic boundary conditions. We can divide this manuscript into six parts. The first section employs the Leray–Schauder alternative to prove the problem’s solution. In the second portion, the analysis of uniqueness is discussed with the help of Banach’s fixed-point theorem. The third section covers both the G-U-H stability and the U-H stability to solve the given generalized Langevin–Sturm–Liouville boundary value problem. The fourth section deals with the variations of the stated problem, the generalized Sturm–Liouville equation with generalized Liouville–Caputo derivatives. The fifth section deals with the variations of the stated problem, the generalized Langevin with generalized Liouville–Caputo derivatives. Lastly, three examples, which serve as applications, are included to demonstrate the highlights of our results
Relative Controllability and Ulam–Hyers Stability of the Second-Order Linear Time-Delay Systems
No full textWe introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to obtain a closed form solution to IVP for a second-order time-delayed linear system with noncommutative matrices A and Ω. We also introduce a delay Gramian matrix and examine a relative controllability linear/semi-linear time delay system. We have obtained the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system. In addition, we have obtained sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam–Hyers stability of a second-order semi-linear time-delayed system
Nonlinear sequential fractional differential equations with nonlocal boundary conditions
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