Abstract
The existence of symmetric-periodic outcomes for a class of fractional differential equations has been increasingly studied. Such study has used various methods such as fixed point theory, critical point theory, and approximation theory. In this work, we study the m-pseudo almost automorphic (m-P $$\Lambda \Lambda$$ ) outcomes for a category of fractional neutral differential equations. To satisfy this aim, we introduce composition results under suitable conditions and employ them to establish some extant outcomes using interpolation theory mixed with fixed point technique. Examples are illustrated.
Highlights
The symmetry in the field of differential equations is a transformation that preserves its domestic of results invariant
Chang and Luos [16] presented a composition theorem for m-PKK function, which was proved under appropriate conditions
The aim of this paper is to study the existence of periodic solutions for the following Fractional differential equations (FDEs): Dl tðtÞ þ uðt; tðtÞÞ 1⁄4 KtðtÞ þ #ðt; tðtÞÞ; t 2 R ð1Þ
Summary
The symmetry in the field of differential equations is a transformation that preserves its domestic of results invariant. V is stated to be m-PKK if u comes in the form u 1⁄4 # þ U; where # 2 KKðR; vÞ and U 2 fðR; v; mÞ: So, all such functions have a space denoted by qKKðR; v; mÞ: Most clearly, we have KKðR; vÞ & qKKðR; v; mÞ & BCðR; vÞ: Lemma 2.5 [20, Theorem 2.2.6] If u : R Â v7!v is PKK, and assume that uðt; Þ is uniformly continuous on each bounded subset j & v uniformly for t 2 R, that is for any f [ 0; there exists S [ 0 such that x; y 2 j and kx À yk\S imply that kuðt; xÞ À uðt; yÞk\f for all t 2 R.
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