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On a new variant of cyclic (noncyclic) condensing operators with existence of optimal solutions to an FDE

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper is designed to highlight the presence of an optimal solution to a differential system comprising fractional order derivatives, precisely the ψ-Caputo derivative, under the prescribed initial constraints. This is attained through a new variant of cyclic (noncyclic) condensing operators incorporating a pair of maps. The altered notion facilitates in evolving best proximity point (pair) results as well as coupled best proximity point results with supportive corollaries.
Wydawca
Rocznik
Strony
393--406
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
  • Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India
  • Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
  • Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India
Bibliografia
  • [1] R. R. Akhmerov, M. I. Kamenskiĭ, A. S. Potapov, A. E. Rodkina and B. N. Sadovski˘ı, Measures of Noncompactness and Condensing Operators, Oper. Theory Adv. Appl. 55, Birkhäuser, Basel, 1992.
  • [2] R. Almeida, A. B. Malinowska and M. T. T. Monteiro, Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications, Math. Methods Appl. Sci. 41 (2018), no. 1, 336-352.
  • [3] K. Amiri, M. Khanehgir and M. Mursaleen, Solution of infinite system of third-order three-point nonhomogeneous boundary value problem in weighted sequence space bvωp , Rend. Circ. Mat. Palermo Ser. II (2023), DOI 10.1007/s12215-023-00986-1.
  • [4] J. M. Ayerbe Toledano, T. Domínguez Benavides and G. López Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Oper. Theory Adv. Appl. 99, Birkhäuser, Basel, 1997.
  • [5] J. Banaś and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, New Delhi, 2014.
  • [6] A. Das, R. Jain and H. K. Nashine, A fixed point result via new condensing operator and its application to a system of generalized proportional fractional integral equations, J. Pseudo-Differ. Oper. Appl. 14 (2023), no. 2, Paper No. 21.
  • [7] A. Das, M. Paunović, V. Parvaneh, M. Mursaleen and Z. Bagheri, Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness, Demonstr. Math. 56 (2023), no. 1, Article ID 20220192.
  • [8] K. Deimling, Nonlinear Functional Analysis, Courier Corporation, New York, 2010.
  • [9] K. Diethelm, Erratum: The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus, Fract. Calc. Appl. Anal. 20 (2017), no. 6, 1567-1570.
  • [10] M. Gabeleh, Best proximity points for cyclic mappings, Thesis, 2012.
  • [11] M. Gabeleh, E. Malkowsky, M. Mursaleen and V. Rakočević, A new survey of measures of noncompactness and their applications, Axioms 11 (2022), 299-365.
  • [12] M. Gabeleh and J. Markin, Optimum solutions for a system of differential equations via measure of noncompactness, Indag. Math. (N. S.) 29 (2018), no. 3, 895-906.
  • [13] M. Gabeleh and J. Markin, Global optimal solutions of a system of differential equations via measure of noncompactness, Filomat 35 (2021), no. 15, 5059-5071.
  • [14] M. Gabeleh and C. Vetro, A new extension of Darbo’s fixed point theorem using relatively Meir-Keeler condensing operators, Bull. Aust. Math. Soc. 98 (2018), no. 2, 286-297.
  • [15] B. Hazarika, H. M. Srivastava, R. Arab and M. Rabbani, Existence of solution for an infinite system of nonlinear integral equations via measure of noncompactness and homotopy perturbation method to solve it, J. Comput. Appl. Math. 343 (2018), 341-352.
  • [16] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
  • [17] E. Zeidler, Nonlinear Functional Analysis and its Applications. I: Fixed Point Theorems, Springer, New York, 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8547f161-b631-4a12-b68a-5eaf4cbf831b
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