Abstract
This paper gives some novel generalizations by considering the generalized conformable fractional integrals operator for reverse Minkowski type and reverse Hölder type inequalities. Furthermore, novel consequences connected with this inequality, together with statements and confirmation of various variants for the advocated generalized conformable fractional integral operator, are elaborated. Moreover, our derived results are provided to show comparisons of convergence between old and modified operators towards a function under different parameters and conditions. The numerical approximations of our consequence have several utilities in applied sciences and fractional integro-differential equations.
Highlights
Fractional calculus, generally referred to as the calculus of non-integer order, was a trademark outgrowth of traditional definitions of calculus integral and derivative
We state some of them, that is, the variants of Minkowski, Hardy, Opial, Hermite–Hadamard, Grüss, Lyenger, Wrtinger, Ostrowski, Čebyšev and Pólya–Szegö [53,54,55,56,57,58,59]. Such applications of fractional integral operators compelled us to show the generalization of the reverse Minkowski inequality [43, 44, 53] involving generalized conformable fractional integrals operators
This section comprises our principal involvement of establishing the proof of the reverse Minkowski inequalities via generalized conformable fractional integral operators defined in (2.1) and (2.2) and an associated theorem insinuated as the reverse Minkowski inequalities
Summary
Fractional calculus, generally referred to as the calculus of non-integer order, was a trademark outgrowth of traditional definitions of calculus integral and derivative. We state some of them, that is, the variants of Minkowski, Hardy, Opial, Hermite–Hadamard, Grüss, Lyenger, Wrtinger, Ostrowski, Čebyšev and Pólya–Szegö [53,54,55,56,57,58,59] Such applications of fractional integral operators compelled us to show the generalization of the reverse Minkowski inequality [43, 44, 53] involving generalized conformable fractional integrals operators. This section comprises our principal involvement of establishing the proof of the reverse Minkowski inequalities via generalized conformable fractional integral operators defined in (2.1) and (2.2) and an associated theorem insinuated as the reverse Minkowski inequalities.
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