F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Advance in Di_erence Equations, Vol.247, (2017).
K. Diethelm, The Analysis of Fractional Di_erential Equations, Lecture Notes in Mathematics, (2010).
R. Hilfer, Applications of Fractional Calculus in Physics, Word Scienti_c, Singapore, (2000).
A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Matematics Studies, Vol. 204 (2006).
R.L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, Redding, (2006).
I. Podlubny, Fractional Di_erential Equations, Academic Press, San Diego, (1999).
S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon & Breach, Yverdon, (1993).
U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., Vol.218, pp.860-865, (2011).
U.N Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., Vol.6, pp.1-15, (2014).
T. Abdeljawad, On conformable fractional calculus, J.Comput. Appl. Math., Vol.279, pp.57-66, (2015).
A.A Kilbas, Hadamard type fractional calculus, J. Korean Math. Soc., Vol.38, pp.1191-1204, (2001).
Y.Y. Gambo, F. Jarad, T. Abdeljawad, D. Baleanu, On Caputo modi_cation of the Hadamard fractional derivate. Adv. Di_er.Equ., Vol.2014, No.10 (2014).
F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modi_cation of the Hadamard fractional derivative, Adv. Di_er. Equ., Vol.142 (2012).
Y. Adjabi, F. Jarad, D. Baleanu, T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, J.Comput. Anal. Appl., Vol.21, No.1, pp.661-681 (2016).
F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modi_cation. J., Nonlinear Sci. Appl., Vol.10, No.5, pp.2607-2619 (2017).
A. Akkurt, H. Yıldırım, On Hermite-Hadamard-Fej_er type inequalities for convex functions via fractional integrals, Mathematica Moravica, Vol.21, No.1, pp.105-123 (2017).
H. Yıldırım, Z. Kırtay, Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities, Malaya Journal of Matematik, Vol.2, No.3, pp.322-329 (2014).
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., Vol.279, pp.57- 66 (2015).
L.G. Zivlaei, A.B. Mingarelli, On the Basic Theory of Some Generalized and Fractional Derivatives, Fractal and Fractional, Vol.6, No.672 (2022).
M. Tarıq, K.S. Ntouyas, A.A. Shaikh, New variant of Hermite-Hadamard, Fej_er and Pachpatte-Type Inequality and Its Re_nements Pertaining to Fractional Integral operator, Fractal and Fractional, Vol.7, No.405 (2023).
E. Kaçar, Z. Kaçar, H. Yıldırım, Integral inequalities for Riemann-Liouville Fractional Integral of a Function with Respeect to Another Function, Iran J. Matth Sci Inform. Vol.13, pp.1-13 (2018).
In this paper, we introduce the concepts of left and right generalized conformable fractional integrals, alongside the corresponding derivatives.
Additionally, we extend our investigation to derive the generalized conformable derivatives for functions within specific spaces, elucidating their inherent properties.
F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Advance in Di_erence Equations, Vol.247, (2017).
K. Diethelm, The Analysis of Fractional Di_erential Equations, Lecture Notes in Mathematics, (2010).
R. Hilfer, Applications of Fractional Calculus in Physics, Word Scienti_c, Singapore, (2000).
A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Matematics Studies, Vol. 204 (2006).
R.L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, Redding, (2006).
I. Podlubny, Fractional Di_erential Equations, Academic Press, San Diego, (1999).
S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon & Breach, Yverdon, (1993).
U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., Vol.218, pp.860-865, (2011).
U.N Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., Vol.6, pp.1-15, (2014).
T. Abdeljawad, On conformable fractional calculus, J.Comput. Appl. Math., Vol.279, pp.57-66, (2015).
A.A Kilbas, Hadamard type fractional calculus, J. Korean Math. Soc., Vol.38, pp.1191-1204, (2001).
Y.Y. Gambo, F. Jarad, T. Abdeljawad, D. Baleanu, On Caputo modi_cation of the Hadamard fractional derivate. Adv. Di_er.Equ., Vol.2014, No.10 (2014).
F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modi_cation of the Hadamard fractional derivative, Adv. Di_er. Equ., Vol.142 (2012).
Y. Adjabi, F. Jarad, D. Baleanu, T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, J.Comput. Anal. Appl., Vol.21, No.1, pp.661-681 (2016).
F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modi_cation. J., Nonlinear Sci. Appl., Vol.10, No.5, pp.2607-2619 (2017).
A. Akkurt, H. Yıldırım, On Hermite-Hadamard-Fej_er type inequalities for convex functions via fractional integrals, Mathematica Moravica, Vol.21, No.1, pp.105-123 (2017).
H. Yıldırım, Z. Kırtay, Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities, Malaya Journal of Matematik, Vol.2, No.3, pp.322-329 (2014).
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., Vol.279, pp.57- 66 (2015).
L.G. Zivlaei, A.B. Mingarelli, On the Basic Theory of Some Generalized and Fractional Derivatives, Fractal and Fractional, Vol.6, No.672 (2022).
M. Tarıq, K.S. Ntouyas, A.A. Shaikh, New variant of Hermite-Hadamard, Fej_er and Pachpatte-Type Inequality and Its Re_nements Pertaining to Fractional Integral operator, Fractal and Fractional, Vol.7, No.405 (2023).
E. Kaçar, Z. Kaçar, H. Yıldırım, Integral inequalities for Riemann-Liouville Fractional Integral of a Function with Respeect to Another Function, Iran J. Matth Sci Inform. Vol.13, pp.1-13 (2018).