Solvability of infinite systems of fractional differential equations in the space of tempered sequence space $m^\beta(\phi)$

[1] A. Aghajani, J. Bana´s and Y. Jalilian, Existence of solution for a class of nonlinear Volterra singular integral equation, Comput. Math. Appl. , 62 (2011) 1215-1227.

[2] A. Aghajani, M. Mursaleen and A. Shole Haghighi, Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness, Acta Math. Sci. , 35B(3) (2015) 552–566.

[3] A. Aghajani, E. Pourhadi and J.J. Trujillo, Application of measure of noncompactness to a Cauchy problem for fractional differential equation in Banach spaces, Fract. Calc. Appl. Anal., 16(4) (2003) 962—977.

[4] R. Arab, R. Allahyari and A. Shole Haghighi, Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness, Appl. Math. Comput., 246 (2014) 283-291.

[5] J. Bana´s and K. Goebel, Measure of noncompactness in Banach spaces, Lecture notes in pure and applied mathematics. vol. 60. New York: Marcel Dekker, (1980).

[6] J. Bana´s and D. O’Regan, On existence and local attractivity of solutions of a quadratic Volterra integral equation of fraction order, J. Math. Anal. Appl. , 345 (2008) 573-582.

[7] J. Bana´s M. and Mursaleen, Sequence spaces and measures of noncompactness with applications to differential and integral equations, New Delhi: Springer, 2014.

[8] E. Cuesta and J.F Codes, Image processing by means of a linear integro differential equation Visualization imaging and image processing (2003), paper 91, Clagary, (2003). Hamza MH, editor. Acta Press.

[9] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend Sem Mat Univ Padova., 24 (1955) 84–92.

[10] W. Deng, Short memory principal and a predictor-corrector approach for fractional differential equations, J. Comput. Appl. Math., 206 (2007) 174–188.

[11] K. Diethelm, The analysis of fractional differential equations An application-oriented exposition using differential operators of Caputo type, Springer Science Business Media (2010).

[12] L.S. Goldenˇstein, L.T. Gohberg and A.S. Murkus, Investigations of some properties of bounded linear operators with their q-norms, Uˇcen. Zap. Kishinevsk. Uni. , 29 (1957) 29-36.

[13] L.S. Goldenˇstein and A.S. Murkus, On a measure of noncompactness of bounded sets and linear operators, Studies in Algebra and Math. Anal. Kishinev, (1965) 45-54.

[14] B. Hazarika, E. Karapınar, R. Arab and M. Rabbani, Metric-like spaces to prove existence of solution for nonlinear quadratic integral equation and numerical method to solve it, J. Comput. Appl. Math., 328 (15)(2018) 302–313.

[15] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Publishers, vol. 204, 2006.

[16] K. Kuratowski, Sur les espaces complets, Fund. Math., 15 (1930) 301-309.

[17] K. Maleknejad, P. Torabi and R. Mollapourasl, Fixed point method for solving nonlinear quadratic Volterra integral equations, Comput. Math. Appl., 62 (2011) 2555-2566.

[18] A. Meir and E.A. Keeler, Theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969) 326–329.

[19] M. Mursaleen, Application of measure of noncompactness to infinite system of differential equations, Canad. Math. Bull., 56 (2013) 388-394.

[20] M. Mursaleen, Some geometric properties of a sequence space related to lp, Bull. Austral. Math. Soc. , 67 (2003) 343-347.

[21] M. Mursaleen, Differential equations in classical sequence spaces, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 111(2) (2017) 587–612.

[22] M. Mursaleen and A. Alotaibi, Infinite system of differential equations in some BK spaces, Abstract Appl. Anal., Volume 2012, Article ID 863483, 20 pages.

[23] M. Mursaleen, B. Bilalov and S.M.H. Rizvi, Applications of measure of noncompactness to infinite system of fractional differential equations, Filomat. 31 (11) (2017) 3421–3432.

[24] I. Podlubny, Fractional order systems and fractional order controllers, Technical report of-03-94. Institute of Experimental Physics, Slovak Acad. of Sci.; (1994).

[25] I. Podlubny, Fractional Differential Equations An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, vol. 198, 1998.

[26] M. Rabbani, A. Das, B. Hazarika and R. Arab, Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations, Chaos, Solitons and Fractals 140 (2020) 110221.

[27] W.L.C Sargent, Some sequence spaces related to the HP spaces, J. London Math. Soc. 35 (1960) 161-171.