Solution of infinite system of fourth order differential equations in $\ell_{p}$ space.

Abstract

The main objective of this paper is to investigate the solution of infinite system of fourth order differential equations in $\ell_p$ space by using measures of noncompactness. The result is demonstrated with an example.

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References

R.P.Agarwal, M.Benchohra and S.Hamani., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Applicandae Mathematicae, 109(3), 973-1033, 2010.

A.Aghajani, M.Mursaleen and A.S.Haghighi., Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta Mathematica Scientia, 35(3), 552-566, 2015.

A.Aghajani and E.Pourhadi., Application of measure of noncompactness to ℓ1-solvability of infinite systems of second order differential equations, Bulletin of the Belgian Mathematical Society-Simon Stevin, 22(1), 105-118, 2015.

J.Banaś., On measures of noncompactness in Banach spaces, Commentationes Mathematicae Universitatis Carolinae, 21(1), 131-143, 1980.

J.Banaś and M.Lecko., Solvability of infinite systems of differential equations in Banach sequence spaces, Journal of Computational and Applied Mathematics, 137(2), 363-375, 2001.

J.Banaś, M.Mursaleen and S.M.Rizvi., Existence of solutions to a boundary-value problem for an infinite system of differential equations, Electronic Journal of Differential Equations, 262(2017), 1-12, 2017.

J.Banaś and M.Mursaleen., Sequence spaces and measures of noncompactness with applications to differential and integral equations, New Delhi: Springer, (2014).

G.Darbo., Punti uniti in trasformazioni a codominio non compatto, Rendiconti del Seminario matematico della Università di Padova, 24, 84-92, 1955.

G.D.Duffy., Green’s Function with Applications, Chapman and Hall/CRC, London, 2004.

G.Goes and S.Goes., Sequences of bounded variation and sequences of Fourier coefficients, I. Mathematische zeitschrift, 118(2), 93-102, 1970.

T.Jalal and I.A.Malik., Applicability of Measure of Noncompactness for the Boundary Value Problems in ℓp Spaces, Recent Trends in Mathematical Modeling and High Performance Computing, Birkhäuser, Cham, 419-432, 2021,

M.Jleli and B.Samet, B., Existence of positive solutions to a coupled system of fractional differential equations, Mathematical Methods in the Applied Sciences, 6(38),1014-1031, 2015.

K.Kuratowski., Sur les espaces complets, Fundamenta Mathematicae, 1(15), 301-309, 1930.

M.Kirişci., Integrated and differentiated sequence spaces, Journal of Nonlinear Analysis and Application, 2015(1), 2-16, 2015.

I.A.Malik and T.Jalal., Existence of solution for system of differential equations in co and ℓ1 spaces, Afrika Matematika, 31(7), 1129-1143, 2020.

I.A.Malik and T.Jalal., Boundary value problem for an infinite system of second order differential equations in ℓp spaces, Mathematica Bohemica, 1459(2), 1-14, 2019.

I.A.Malik and T.Jalal., Measures of Noncompactness in N¯ q ∆− Summable Difference Sequence Spaces, Journal of Mathematical Extension, 13, 143-159, 2019.

I.A.Malik and T.Jalal., Measures of Noncompactness in N¯(p, q) Summable Sequence Spaces, Operators and Matrices, 13(4), 1191-1205, 2019.

A.Meir and E.Keeler., A theorem on contraction mappings, Journal of Mathematical Analysis and Applications, 28(2), 326-329, 1969.

S.A.Mohiuddine H.M.Srivastava and A.Alotaibi., Application of measures of noncompactness to the infinite system of second-order differential equations in ℓp spaces, Advances in Difference Equations, 2016(1), 1-13, 2016

V.Muresan., Volterra integral equations with iterations of linear modification of the argument, Novi Sad Journal of Mathematics, 33(2), 1-10, 2003.

M.Mursaleen and S.Rizvi., Solvability of infinite systems of second order differential equations in c0 and ℓ1 by MeirKeeler condensing operators, Proceedings of the American Mathematical Society, 144(10), 4279-4289, 2016.

I.M.Olaru., An integral equation via weakly Picard operators. Fixed Point Theory, 11(1), 97-106, 2010.

E.Pourhadi, M.Mursaleen, R.Saadati., On a Class of Infinite System of Third-Order Differential Equations in ℓp via Measure of Noncompactness , Filomat, 3861-3870, 2020.

R.Saadati, E.Pourhadi, M.Mursaleen., Solvability of infinite systems of third-order differential equations in c0 by Meir-Keeler condensing operators , Journal of Fixed Point Theory and Applications, 21(2), 1-6, 2019.

H.M.Srivastava, A.Das, B.Hazarika and S.A.Mohiuddine., Existence of solutions of infinite systems of differential equations of general order with boundary conditions in the space c0 and ℓ1 via the measure of noncompactness, Mathematical Methods in the Applied Sciences, 41(10), 3557-3569, 2018

Published
2024-05-02
Section
Articles