What does "applying classical Indian aesthetics to literary and cultural studies" mean?
If I understand you correctly, you are asking about aesthetics in relation to cultural fiction and traditional literary fiction. If so, then it is first necessary to know what "classical Indian aesthetics" is. When applied to literature, aesthetics are the cohesive set of principles and concepts that comprise the philosophy of what makes literary art and how literary art functions to affect peoples' consciousness. The aesthetics of literature is a very complex concept. In addition, individual schools or periods of literature have their own systems of aesthetics. For example, both English Romantic poets and Indian classical authors have their own aesthetics. In addition to this, individual authors have their own aesthetics. For example, Edmund Spenser has a definitive aesthetic as does R. K. Narayan. These aesthetics will always be unique to each, though there will be overlap with their literary period, school of literary theory, and contemporaries.
The period relevant is the classical period in Indian literature. It is secondly necessary to know the elemental fundamentals of the aesthetic of classical Indian literature. The introductory page of an article on JSTOR (which you can fully access through your school's or university's subscription) provides a statement of these fundamental principles. As Radhakamal Mukerjee says, Indian literature, with religion and metaphysics as its basis and aim, is built around Bharata's second century concept of rasa, which is the "flavor" that idealized "moods, sentiments, and emotions" provide literary works. This is a concept similar to Aristotle's concept of the divinely inspired poet writing mimeses (imitations) of divine truths for which human hearts crave and from which humans are instructed in living according to divine truths and precepts. Mukerjee confirms this illustrative comparison when he says Indian literature is "characterized by ... that which does not belong to this world." It is characterized by "universal ... sentiments and emotions" that the artist depicts in order to attain or offer "supreme bliss."
To apply this to literary fiction and cultural fiction leads to two different end results. Cultural literature is contemporary and seeks to conceal nothing of suffering while revealing everything pertaining to cultural injustice. A very popular branch of cultural literature is post-colonial literature in which the liberated colonized people find and give voice to their suffering. An example of this is Farming of Bones. In this there is no rasa; there is no divine inspiration expressed in sentiment, moods, and emotion, no "supreme bliss" to be attained.
Literary fiction, on the other hand, is predicated on forwarding universal understanding of the human condition, human "sentiments and emotions." Granted, the acknowledged source of inspiration changed from Aristotle's long ago asserted divine truth. For the Romantics, nature was the source of inspiration. For postmodernists, self is the source of inspiration. Yet in each era, the devotion has been to what classical Indian aesthetics calls rasa. An example of this aesthetic is "The Astrologer's Day" by Narayan. Born in 1906, Narayan lived through both colonization and post-colonization; modernism and postmodernism. Yet, his stories reveal rasa: universal qualities relating to the human struggle provide the focal points, universal qualities such as forgiveness, self-control, and mercy, as "The Astrologer's Day" illustrates.