An application to a system of fractional hybrid differential equations of best proximity point (pair) theorems via measure of noncompactness

[1] R.R. Akhmerov, M.I. Kamenskii, A.S. Potapov, A.E. Rodkina, and B.N. Sadovskii, Measures of Noncompactness and Condensing Operators, Vol. 55, Birkhauser, Basel, 1992.

[2] J. Bana´s and K. Goebel, Measure of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 60, Marcel Dekker, New York, 1980.

[3] A. Das, M. Paunovic, 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, Demonst. Math. 56 (2023), no. 1, 20220192.

[4] K. Diethelm, The mean value theorem and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus, Fractional Cal. Appl. Anal. 15 (2012), 304–313.

[5] M.A.E. Herzallah and D. Baleanu, On fractional order hybrid differential equations, Abstr. Appl. Anal. 2014 (2014), Article ID 389386, 7 pages.

[6] 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.

[7] 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), no. 1, 341–352.

[8] B. Hazarika, H. M. Srivastava, R. Arab, and M. Rabbani, Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution, Appl. Math. Comput. 360 (2019), no. 1, 131–146.

[9] S.A. Mohiuddine, H.M. Srivastava, and A. Alotaibi, Application of measures of noncompactness to the infinite system of second-order differential equations in ℓ_p space, Adv. Difference Equ. 2016 (2016), no. 1, 317.

[10] H. K. Nashine, R. Arab, P.R. Patle, and D.K. Patel, Best proximity point results via measure of noncompactness and application, Numerical Funct. Anal. Optim. 42 (2021), no. 4, 430–442.

[11] P.R. Patle, M. Gabeleh, V. Rakocevic, and M.E. Samei, New best proximity point(pair) theorems via MNC and application to the existence of optimum solutions for a system of ψ-Hilfer fractional differential equations, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117 (2023), 124.

[12] 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 spaces c0 and l1 via the measure of noncompactness, Math. Meth. Appl. Sci. 41 (2018), no. 10, 3558–3569.

[13] H.M. Srivastava, A. Deep, S. Abbas, and B. Hazarika, Solvability for a class of generalized functional-integral equations by means of Petryshyn’s fixed point theorem, J. Nonlinear Convex Anal. 22 (2021), no. 12, 2715–2737.