A5101849731- Fractional Differential Equations Solutions
- Nonlinear Differential Equations Analysis
- Iterative Methods for Nonlinear Equations
- Nonlinear Waves and Solitons
- Differential Equations and Boundary Problems
- Mathematical and Theoretical Analysis
- Differential Equations and Numerical Methods
- Mathematical functions and polynomials
- Functional Equations Stability Results
- Numerical methods in engineering
- Algebraic and Geometric Analysis
- Chaos control and synchronization
- Mathematical Inequalities and Applications
- Sports and Physical Education Studies
- Higher Education Teaching and Evaluation
- Philosophical Thought and Analysis
- Physical Education and Sports Studies
- Nanofluid Flow and Heat Transfer
- Developmental and Educational Neuropsychology
- Vascular Tumors and Angiosarcomas
- Railway Systems and Energy Efficiency
- PI3K/AKT/mTOR signaling in cancer
- Electric Vehicles and Infrastructure
- Learning Styles and Cognitive Differences
- Physical Education and Pedagogy
Universidad Politécnica de Cartagena
2003-2025
Hospital Universitario Nuestra Señora de Candelaria
2022
Hospital Universitario La Paz
2019
Universidad Autónoma de Madrid
2019
Sorbonne Université
2012
A nonlinear quantum boundary value problem (q-FBVP) formulated in the sense of Caputo derivative, with fractional q-integro-difference conditions along its quantum-difference inclusion q-BVP are investigated this research. To prove solutions’ existence for these systems, we rely on notions such as condensing functions and approximate endpoint criterion (AEPC). Two numerical examples provided to apply validate our main results research work.
In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled Adomian decomposition method has been defined applied to solve newly dispersion. The approximate analytical solutions are obtained compared each other graphically.
Abstract An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The ML–Hyers–Ulam stability established investigation. We study both of the Hyers–Ulam (HUS) and ML–Hyers–Ulam–Rassias (ML-HURS) detail for our proposed differential (DEq). Our technique unifies various equations’ classes. Therefore, can be further applied future research works with applications to science engineering.
In this article, the optimal auxiliary function method (OAFM) is extended to general partial differential equations (PDEs). Our proposed highly efficient and provides means of controlling approximate solution's convergence. Illustrative examples are provided prove exceptional consistency PDEs' analytical numerical solutions. OAFM practically very effective where with only one iteration, a fast convergence guaranteed. considered reliable technique high accuracy in finding solutions for such...
This paper addresses the extension of Martinez–Kaabar fractal–fractional calculus (simply expressed as MK calculus) to context reduced differential transformation, with applications solution some partial equations. Since this transformation is derived from Taylor series expansion real-valued functions several variables, it necessary develop theory in such functions. Firstly, classical elements analysis real variables are introduced, concept derivative and Clairaut’s theorem, terms...
Most European Union governments and numerous railway operators have announced plans to replace most of their diesel units by 2030–2040. However, a significant portion the rail network remains non-electrified. In some cases, proposed solution has been close certain tracks, but this approach entails considerable societal costs for small cities represents loss prior investments. Consequently, hybrid locomotives multiple (either new or refurbished) emerge as viable during transitional period...
A newly proposed generalized formulation of the fractional derivative, known as Abu-Shady-Kaabar is investigated for solving differential equations in a simple way. Novel results on this definition and verified, which complete theory introduced so far. In particular, chain rule, some important properties derived from mean value theorem, derivation inverse function are established context. Finally, we apply obtained to implicitly defined parametrically functions. Likewise, study version fixed...
<abstract> A new theory of analytic functions has been recently introduced in the sense conformable fractional derivative. In addition, concept contour integral also developed. this paper, we propose and prove some results on complex integration. First, establish necessary sufficient conditions for a continuous function to have antiderivative sense. Finally, well-known Cauchy′s theorems will be subject extension that do paper. </abstract>
We investigate the existence of solutions for a system m-singular sum fractional q-differential equations in this work under some integral boundary conditions sense Caputo q-derivatives. By means fixed point Arzelá–Ascoli theorem, positive is obtained. providing examples involving graphs, tables, and algorithms, our fundamental result about endpoint illustrated with given computational results. In general, symmetry q-difference have common correlation between each other. Lie algebra,...
Abstract In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions’ existence for class nonlinear q-difference equations in the context Riemann–Liouville q-derivative on an infinite interval. The system’s solution formulated with help Green’s function. A compactness criterion established special space. All obtained results uniqueness and are fixed-point theorems. Some essential examples illustrated to support our main outcomes.
In the present research study, for a given multiterm boundary value problem (BVP) involving nonlinear fractional differential equation (NnLFDEq) of variable order, uniqueness-existence properties are analyzed. To arrive at such an aim, we first investigate some specifications this kind order operator and then derive required criteria confirming existence solution. All results in study established with help two fixed-point theorems examined by practical example.
In this paper, the existence of solution and its stability to fractional boundary value problem (FBVP) were investigated for an implicit nonlinear differential equation (VOFDE) variable order. All criteria solutions in our establishments derived via Krasnoselskii’s fixed point theorem sequel, Ulam–Hyers–Rassias (U-H-R) is checked. An illustrative example presented at end paper validate findings.
Abstract We study sequential fractional pantograph q -differential equations. establish the uniqueness of solutions via Banach’s contraction mapping principle. Further, we define and Ulam–Hyers stability Ulam–Hyers–Rassias solutions. also discuss an illustrative example.
In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying definition to some elementary functions, we show its compatibility with the results of FF in Caputo sense power law. The main elements classical differential calculus are introduced terms derivative. Thus, establish and demonstrate basic operations derivatives, chain rule, mean value theorems their immediate applications inverse function’s We complete theory by proposing notion integration presenting...
The conformable derivative and its properties have been recently introduced. In this research work, we propose prove some new results on the calculus. By using definitions derivatives of higher order, generalize theorems mean value which follow same argument as in classical Taylor remainder is obtained through generalized theorem value. Finally, introduce version two interesting multivariable calculus via formula finite increments.
In this paper, a new class of neutral functional delay differential equation involving the generalized <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>ψ</a:mi> </a:math> -Caputo derivative is investigated on partially ordered Banach space. The existence and uniqueness results to given boundary value problem are established with help Dhage’s technique contraction principle. Also, we prove other criteria by means topological degree method. Finally, Ulam-Hyers type stability...
Our main purpose in this paper is to prove the existence of solutions for fractional strongly singular thermostat model under some generalized boundary conditions. In way, we use recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible maps. Further, establish similar results hybrid version given control model. Some examples are studied illustrate consistency our results.
The most important properties of the conformable derivative and integral have been recently introduced. In this paper, we propose prove some new results on Laplace’s equation. We discuss solution mathematical problem with Dirichlet-type Neumann-type conditions. All our obtained will be applied to interesting examples.
Recently, the conformable derivative and its properties have been introduced
Abstract This paper presents the solution of important types non-linear time-fractional partial differential equations via conformable Elzaki transform Homotopy perturbation method. We apply proposed technique to solve four equations. In addition, we establish results on uniqueness and convergence solution. Finally, numerical for a variety α values are briefly examined. The method performs well in terms simplicity efficiency.
The extension of the theory generalized fractal–fractional calculus, named in this article as Martínez–Kaabar Fractal–Fractional (MKFF) is addressed to field integral equations. Based on classic Adomian decomposition method, by incorporating MKFF α,γ-integral operator, we establish so-called extended method (EADM). convergence proposed technique also discussed. Finally, some interesting Volterra Integral equations non-integer order which possess a fractal effect are solved via our approach....
In this present work, the existence and uniqueness of solutions for fractional pantograph differential equations involving Riemann-Liouville Caputo derivatives are established by applying contraction mapping principle Leray-Schauder?s alternative. The Mittag-Leffler-Ulam stability results also obtained via generalized singular Gronwall?s inequality. Finally, we give an illustrative example.
In this article, new results are investigated in the context of recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve generalized Legendre differential equation. As classical case, polynomials constitute notable solutions to aforementioned sense derivative Abu-Shady–Kaabar, establish important properties such as Rodrigues formula and recurrence relations. Special attention is also devoted another very property their orthogonal character. Finally, representation a...
In this research paper, we discuss systems of conformable linear differential equations. The fundamental exponential matrix has been used to express the solution homogeneous and nonhomogeneous systems. method variation parameters investigated find particular system Several illustrative examples have provided at end our study validate all obtained results.