Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

[1]   S. Abbas, M. Benchohra and J. Henderson, Weak solutions for implicit fractional differential equations of Hadamard type, Adv. Dyn. Syst. Appl. 11(3) (2016), 1–13.

[2]   S. Abbas, M. Benchohra, N. Hamidi and J. Henderson, Caputo-Hadamard fractional differential equations in Banach spaces, Fract. Calc. Appl. Anal. 21(4) (2018), 1027–1045.

[3]   Y. Adjabi, F. Jarad, D. Baleanu and T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, Journal of Computational Analysis and Applications 21(4) (2016), 661–681.

[4]   A. Aghajani, E. Pourhadi and J. J. Trujillo, Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces, Fract. Calc. Appl. Anal. 16(4) (2013), 962–977.

[5]   A. Aghajani and E. Pourhadi, Application of measure of noncompactness to ℓ₁-solvability of infinite systems of second order differential equations, Bull. Belg. Math. Soc. Simon Stevin 22(1) (2015), 105–118.

[6]   B. Ahmad, A. Alsaedi, S. K. Ntouyas and J. Tariboon, Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Springer, Cham, 2017.

[7]   A. Ardjouni and A. Djoudi, Positive solutions for nonlinear Caputo-Hadamard fractional differential equations with integral boundary conditions, Open J. Math. Anal. 3(1) (2019), 62–69.

[8]   Y. Arioua and N. Benhamidouche, Boundary value problem for Caputo-Hadamard fractional differential equations, Surv. Math. Appl. 12 (2017), 103–115.

[9]   J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis. John Wiley & Sons, New York, 1984.

[10]   J. M. Ayerbe Toledano, T. Domínguez Benavides and G. López Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhäuser, Basel 1997.

[11]   J. Bana and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.

[12]   J. Bana, M. Jleli, M. Mursaleen, B. Samet and C. Vetro, Advances in nonlinear analysis via the concept of measure of noncompactness, Springer, Singapore, 2017.

[13]   M. Benchohra, J. Henderson and D. Seba, Measure of noncompactness and fractional differential equations in Banach spaces, Comm. Pure Appl. Math. 12(4) (2008), 419–427.

[14]   M. Benchohra, S. Hamani and S. K. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Anal. 71 (2009), 2391–2396.

[15]   M. Benchohra and F.-Z. Mostefai, Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces, Opuscula Math. 32(1) (2012), 31–40.

[16]   M. Benchohra, S. Bouriah and J. J. Nieto, Existence of periodic solutions for nonlinear implicit Hadamard’s fractional differential equations, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 112(1) (2018), 25–35.

[17]   W. Benhamida, S. Hamani and J. Henderson, Boundary value problems for Caputo-Hadamard fractional differential equations, Advances in the Theory of Nonlinear Analysis and its Applications 2 (2018), 138–145.

[18]   W. Benhamida, J. R. Graef and S. Hamani, Boundary value problems for Hadamard fractional differential equations with nonlocal multi-point boundary conditions, Fract. Differ. Calc. 8(1) (2018), 165–176.

[19]   D. Bothe, Multivalued perturbations of m-accretive differential inclusions, Israel J. Math. 108 (1998), 109–138.

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

[21]   C. Derbazi, H. Hammouche and M. Benchohra, Weak solutions for some nonlinear fractional differential equations with fractional integral boundary conditions in Banach spaces, Journal of Nonlinear Functional Analysis 2019 (2019), 1-11.

[22]   Y. Y. Gambo, F. Jarad, D. Baleanu and T. Abdeljawad, On Caputo modification of the Hadamard fractional derivatives, Adv. Difference Equ. 2014 (2014), 12 pages.

[23]   J. Hadamard, Essai sur l’etude des fonctions donnees par leur developpment de Taylor, Journal de Mathématiques Pures et Appliquées 8 (1892), 101-186.

[24]   F. Jarad, T. Abdeljawad and D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ. 2012 (2012), 8 pages.

[25]   H.-P. Heinz, On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlinear Anal. 7(12) (1983), 1351–1371.

[26]   R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing Co. Inc., River Edge, New Jersey, 2000.

[27]   P. Karthikeyan and R. Arul, Integral boundary value problems for implicit fractional differential equations involving Hadamard and Caputo-Hadamard fractional derivatives, Kragujevac J. Math. 45(3) (2021), 331–341.

[28]   A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. 38(6) (2001), 1191–1204.

[29]   A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier Science B.V., Amsterdam, 2006.

[30]   I. A. Malik and T. Jalal, Application of measure of noncompactness to infinite systems of differential equations in ℓ_p spaces, Rend. Circ. Mat. Palermo (2) (2019), DOI 10.1007/s12215-019-00411-6

[31]   K. S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.

[32]   M. Mursaleen and S. A. Mohiuddine, Applications of measures of noncompactness to the infinite system of differential equations in ℓ_p spaces, Nonlinear Anal. 75(4) (2012), 2111–2115.

[33]   M. Mursaleen and S. M. H. Rizvi, Solvability of infinite systems of second order differential equations in c₀ and ℓ₁ by Meir-Keeler condensing operators, Proc. Amer. Math. Soc. 144(10) (2016), 4279–4289.

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

[35]   M. Mursaleen, S. M. H. Rizvi and B. Samet, Solvability of a class of boundary value problems in the space of convergent sequences, Appl. Anal. 97(11) (2018), 1829–1845.

[36]   M. Mursaleen and S. M. H. Rizvi, Existence results for second order linear differential equations in Banach spaces, Appl. Anal. Discrete Math. 12(2) (2018), 481–492.

[37]   R. Saadati, E. Pourhadi and M. Mursaleen, Solvability of infinite systems of third-order differential equations in c₀ by Meir-Keeler condensing operators, J. Fixed Point Theory Appl. 21(2) (2019), 16 pages.

[38]   B. Hazarika, R. Arab and M. Mursaleen, Application measure of noncompactness and operator type contraction for solvability of an infinite system of differential equations in ℓ_p-space, Filomat 33(7) (2019), 2181–2189.

[39]   K. B. Oldham, Fractional differential equations in electrochemistry, Advances in Engineering Software 41(1) (2010), 9–12.

[40]   I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1993.

[41]   J. Sabatier, O. P. Agrawal and J. A. T. Machado, Advances in Fractional Calculus-Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007.

[42]   S. Schwabik and G. Ye, Topics in Banach Space integration, Series in Real Analysis 10, World Scientific Publishing Co. Pte. Ltd., Hackensack, New Jersey, 2005.

[43]   V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg & Higher Education Press, Beijing, 2010.

[44]   J. Tariboon, A. Cuntavepanit, S. K. Ntouyas and W. Nithiarayaphaks, Separated boundary value problems of sequential Caputo and Hadamard fractional differential equations, J. Funct. Spaces 2018, Article ID 6974046, 8 pages.

[45]   J. Wang, L. Lv and Y. Zhou, Boundary value problems for fractional differential equations involving Caputo derivative in Banach spaces, J. Appl. Math. Comput. 38 (2012), 209–224.

[46]   E. Zeidler, Nonlinear Functional Analysis and its Applications, part II/B: Nonlinear Monotone Operators, Springer Verlag, New York, 1989.