Results 51 to 60 of about 1,330 (174)

Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations

, 2012
In this paper, we study a nonlinear fractional q-difference equation with nonlocal boundary conditions. The existence of solutions for the problem is shown by applying some well-known tools of fixed-point theory such as Banach’s contraction principle ...
B. Ahmad, S. Ntouyas, I. Purnaras
semanticscholar   +1 more source

Application of (q, τ)‐Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani, Rabha W. Ibrahim, Khalil Ezzinbi   +2 more
wiley   +1 more source

A note on exp-function method combined with complex transform method applied to fractional differential equations

Advances in Nonlinear Analysis, 2015
In this article, the fractional derivatives in the sense of modified Riemann–Liouville and the exp-function method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Liouville ...
Guner Ozkan, Bekir Ahmet, Bilgil Halis
doaj   +1 more source

Existence and Stability Results for Coupled Fractional Dynamic System with Impulses over Non-uniform Time Domains

Nonautonomous Dynamical Systems, 2022
In this manuscript, we examine the existence, uniqueness and stability results for a coupled fractional dynamical system with impulsive and initial-boundary (IB) conditions on non-uniform time domains by implying the theory of time scales.
Kumar Vipin, Malik Muslim
doaj   +1 more source

Positive solution of a fractional differential equation with integral boundary conditions

Journal of Applied Mathematics and Computational Mechanics, 2018
In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions.
Mohammed S Abdo, Hanan A. Wahash, S. K. Panchal   +2 more
semanticscholar   +1 more source

Trajectory Controllability of Fractional Neutral Stochastic Dynamical Systems of Order α ∈ (1, 2] With Deviating Argument

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
In this manuscript, we establish existence, uniqueness, and trajectory controllability for higher order noninstantaneous impulsive fractional neutral stochastic differential equations. First, solvability and uniqueness results are obtained using a fixed‐point approach with appropriate assumptions on nonlinear functions. Next, we deal with the strongest
Dhanalakshmi Kasinathan, Ravikumar Kasinathan, Ramkumar Kasinathan, Karthikeyan Shanmugasundaram, Dimplekumar Chalishajar, Theodore Simos   +5 more
wiley   +1 more source

Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

Demonstratio Mathematica, 2019
In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem.
Ahmad Manzoor, Zada Akbar, Alzabut Jehad
doaj   +1 more source

Results on the modified degenerate Laplace-type integral associated with applications involving fractional kinetic equations

Demonstratio Mathematica, 2023
Recently, integral transforms are a powerful tool used in many areas of mathematics, physics, engineering, and other fields and disciplines. This article is devoted to the study of one important integral transform, which is called the modified degenerate
Almalki Yahya, Abdalla Mohamed, Abd-Elmageed Hala   +2 more
doaj   +1 more source

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

, 2011
Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period.
Kaslik, Eva, Sivasundaram, Seenith
core   +1 more source

Existence and Stability Results for a Modified Diffusion Equation Involving Atangana–Baleanu–Caputo Fractional Derivative

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article shows another display of the modified diffusion equation of fractional order involving Atangana–Baleanu–Caputo fractional derivative. The manuscript contains three major cases: the existence of a solution, uniqueness of the solution, and Hyers–Ulam stability, which are discussed based on valid theorems in nonlinear analysis.
Maral Sangi, Mohammad Esmael Samei, Arpan Hazra   +2 more
wiley   +1 more source