Results 71 to 80 of about 163 (105)

New Caputo fractional differential equation of higher order on unbounded interval and solvability in the Hölder space C 0 , q ( Ω ) $C^{0,q}(\Omega )$

Journal of Inequalities and Applications
We define a new Caputo fractional differential equation of higher-order on unbounded interval { D α c w ( t ) = f ( t ) , 0 ≤ t < ∞ , w ( 0 ) = w ′ ( 0 ) = w ( 4 ) ( 0 ) = w ( 5 ) ( 0 ) = ⋯ = w ( n ) ( 0 ) = 0 , w ‴ ( 0 ) = ∫ 0 η ( η − s ) α − 1 Γ ( α ...
Hojjatollah Amiri Kayvanloo, Farzaneh Pouladi Najafabadi, Ekrem Savaş, Mohammad Mursaleen   +3 more
doaj   +1 more source

New generalizations of Darbo’s fixed point theorem [PDF]

, 2015
Jin Liang, Longsheng Cai
core   +2 more sources

Some generalizations of Darbo's fixed point theorem under weak topology features with application to a Volterra-type integral equation

Applied General Topology
In this paper, we provide some generalizations of Darbo's fixed point theorem for larger classes of contraction. Our results are investigated under the weak topology of a Banach space using the measure of weak noncompactness. The results presented in the
Mohamed Khazou, Abdelmjid Khchine
doaj   +1 more source

Controllability of Fractional Integro-Differential Equations with Delays and Singular Kernels in Fréchet Spaces

Mathematics
This paper is devoted to the investigation of existence and approximate controllability results for a class of fractional integro-differential equations formulated in Fréchet spaces.
Fatima Mesri, Abdelkrim Salim, Mouffak Benchohra   +2 more
doaj   +1 more source

On 𝑟-separated sets in normed spaces

, 1991
The separation of a bounded set A A in a metric space δ ( A ) \delta (A) is defined as the supremum of the numbers r > 0 r > 0 such that ...
Juan Arias-de-Reyna
core   +1 more source

EXISTENCE RESULT FOR A COUPLED SYSTEM OF HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS IN A BANACH ALGEBRA [PDF]

In this work, we investigate the existence result for a coupled system of hybrid fractional differential equations in a Banach algebra. Our main result is based on a generalization of Darbo’s fixed point theorem in Banach algebra.
Srivastava, Hari Mohan, Hedia, Benaouda
core   +1 more source

Analysis of Implicit Neutral-Tempered Caputo Fractional Volterra–Fredholm Integro-Differential Equations Involving Retarded and Advanced Arguments

Mathematics
This paper investigates a class of implicit neutral fractional integro-differential equations of Volterra–Fredholm type. The equations incorporate a tempered fractional derivative in the Caputo sense, along with both retarded (delay) and advanced ...
Abdulrahman A. Sharif, Muath Awadalla
doaj   +1 more source

Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation

This paper introduces novel fixed-point theorems for generalized Proinov contraction mappings utilizing the measure of noncompactness. These results significantly extend existing contraction principles and provide novel methods for analyzing nonlinear ...
Belhadj, Maha, Stojan Radenović, Stojan, Roshan, Jamal Rezaei   +2 more
core   +1 more source

Geraghty–𝔽-Contraction Type Darbo Fixed-Point Theorems With an Application

Journal of Mathematics
In this study, Darbo’s fixed-point theorem is extended by employing Geraghty–𝔽-contractions on Banach spaces. The obtained results are then applied to establish the existence of solutions for a fractional integral equation in the space C0,ς, equipped ...
Samira Hadi Bonab, Hasan Hosseinzadeh, Reza Alayi, Zoran Mitrovic, Shahla Hosseini   +4 more
doaj   +1 more source