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Non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function
Author(s) -
Abbas Mohamed I.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7419
Subject(s) - mathematics , uniqueness , fractional calculus , contraction mapping , mathematical analysis , nonlinear system , contraction principle , function (biology) , differential equation , contraction (grammar) , type (biology) , fixed point theorem , medicine , ecology , physics , quantum mechanics , evolutionary biology , biology
This paper concerns the existence and uniqueness of solutions of non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function. By the aid of the nonlinear alternative of Leray‐Schauder type and the Banach contraction mapping principle, the main results are demonstrated. Two examples are inserted to illustrate the applicability of the theoretical results.