A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces

被引：0

作者：

Okeke, Godwin Amechi ^{[1
]}

Ugwuogor, Cyril Ifeanyichukwu ^{[1
]}

Alqahtani, Rubayyi T. ^{[2
]}

Kaplan, Melike ^{[3
]}

Ahmed, W. Eltayeb ^{[2
]}

机构：

[1] Fed Univ Technol Owerri, Sch Phys Sci, Dept Math, Funct Anal & Optimizat Res Grp Lab FANORG, PMB 1526, Owerri, Imo, Nigeria

[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[3] Kastamonu Univ, Fac Engn & Architecture, Dept Comp Engn, Kastamonu, Turkiye

来源：

INTERNATIONAL JOURNAL OF MODERN PHYSICS C | 2025年 / 36卷 / 01期

关键词：

Asymptotically generalized Phi-pseudocontractive mappings in the intermediate sense; iterative process; Banach spaces; modified Picard-Ishikawa hybrid iterative process; nonlinear Caputo type fractional differential equations; MAPPINGS;

D O I：

10.1142/S0129183124501766

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We introduce the modified Picard-Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized phi-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard-Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.

引用

页数：19

共 26 条

[1] On the solution of a boundary value problem associated with a fractional differential equation
Sevinik Adiguzel, Rezan
Aksoy, Umit
Karapinar, Erdal
Erhan, Inci M.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 47 (13) : 10928 - 10939
[2] Newton's method on generalized Banach spaces
Argyros, Ioannis K.
Behl, Ramandeep
Motsa, S. S.
[J]. JOURNAL OF COMPLEXITY, 2016, 35 : 16 - 28
[3] Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
Atangana, Abdon
Jose Nieto, Juan
[J]. ADVANCES IN MECHANICAL ENGINEERING, 2015, 7 (10): : 1 - 7
[4] Positive solutions for boundary value problem of nonlinear fractional differential equation
Bai, ZB
Lü, HS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) : 495 - 505
[5] Nonlinear fractional differential equations with integral boundary value conditions
Cabada, Alberto
Hamdi, Zakaria
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 228 : 251 - 257
[6] On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
Chang, SS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 216 (01) : 94 - 111
[7] Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings
Chidume, CE
Chidume, CO
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) : 545 - 554
[8] FIXED-POINTS BY A NEW ITERATION METHOD
ISHIKAWA, S
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (01) : 147 - 150
[9] Convergence and Stability of a Novel M-Iterative Algorithm with an Application
Kaur, Manjinder
Chandok, Sumit
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2022, 2022
[10] Kim J. K., 2009, NONLINEAR ANAL, V71, P2883

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